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2024
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Lecture notes on Malliavin calculus in regularity structures
inJournal
2023
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Bias in the representative volume element method : periodize the ensemble instead of its realizations
In: Foundations of computational mathematics, (2023)inJournal
2023
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Thermodynamically consistent and positivity-preserving discretization of the thin-film equation with thermal noise
In: Mathematics of computation, 92 (2023), pp. 1931-1976Preprint
2023
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Almost sharp rates of convergence for the average cost and displacement in the optimal matching problem
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2023
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There is no stationary \(p\)-cyclically monotone Poisson matching in 2D
inJournal
2023
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There is no stationary cyclically monotone Poisson matching in 2d
In: Probability theory and related fields, 187 (2023) 3/4, pp. 629-656inJournal
2023
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Variational methods for a singular SPDE yielding the universality of the magnetization ripple
In: Communications on pure and applied mathematics, 76 (2023) 11, pp. 2959-3043Preprint
2023
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Lecture notes on the harmonic approximation to quadratic optimal transport
inJournal
2023
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The structure group for quasi-linear equations via universal enveloping algebras
In: Communications of the American Mathematical Society, 3 (2023), pp. 1-64Preprint
2023
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Convergence to the planar interface for a nonlocal free-boundary evolution
inJournal
2023
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Lecture notes on tree-free regularity structures
In: Matemática contemporÒanea, 58 (2023), pp. 150-196inJournal
2022
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Uniform energy distribution in a pattern-forming system of surface charges
In: Revista Matemática Iberoamericana, 38 (2022) 3, pp. 783-822Preprint
2022
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The Gaussian free-field as a stream function : asymptotics of effective diffusivity in infra-red cut-off
inJournal
2022
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Erratum to [updated to open access] : 'On the existence of the Green function for elliptic systems in divergence form' [In: Manuscripta mathematica, 167 (2022) 1/2, p. 385-402]
In: Manuscripta mathematica, 167 (2022) 1/2, pp. 403-404inJournal
2022
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On the existence of the Green function for elliptic systems in divergence form
In: Manuscripta mathematica, 167 (2022) 1/2, pp. 385-402inJournal
2022
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Arbeitsgemeinschaft : Quantitative stochastic homogenization ; 16 October - 22 October 2022 ; report no. 48/2022
In: Oberwolfach reports, 19 (2022) 4, pp. 2741-2809inJournal
2022
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The annealed Calderon-Zygmund estimate as convenient tool in quantitative stochastic homogenization
In: Journal of functional analysis, 283 (2022) 7, p. 109594Preprint
2022
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A tree-free approach to regularity structures : the regular case for quasi-linear equations
inJournal
2022
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Representative volume elements for matrix-inclusion composites : a computational study on the effects of an improper treatment of particles intersecting the boundary and the benefits of periodizing the ensemble
In: Journal of the mechanics and physics of solids, 158 (2022), p. 104652inJournal
2021
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Quantitative estimates in stochastic homogenization for correlated coefficient fields
In: Analysis and PDE, 14 (2021) 8, pp. 2497-2537inJournal
2021
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Quantitative linearization results for the Monge-Ampère equation
In: Communications on pure and applied mathematics, 74 (2021) 12, pp. 2483-2560Preprint
2021
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A diagram-free approach to the stochastic estimates in regularity structures
inJournal
2021
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Optimal artificial boundary condition for random elliptic media
In: Foundations of computational mathematics, 21 (2021) 6, pp. 1643-1702Preprint
2021
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Optimal artificial boundary conditions based on second-order correctors for three dimensional random elliptic media
inJournal
2021
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Sharp boundary \(\varepsilon\)-regularity of optimal transport maps
In: Advances in mathematics, 381 (2021), p. 107603Preprint
2021
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A priori bounds for quasi-linear SPDEs in the full sub-critical regime
inJournal
2021
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Variational approach to regularity of optimal transport maps : general cost functions
In: Annals of PDE, 7 (2021) 2, p. 17inJournal
2020
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Effective multipoles in random media
In: Communications in partial differential equations, 45 (2020) 6, pp. 561-640inJournal
2020
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Higher-order pathwise theory of fluctuations in stochastic homogenization
In: Stochastics and partial differential equations : analysis and computations, 8 (2020) 3, pp. 625-692inJournal
2020
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Robustness of the pathwise structure of fluctuations in stochastic homogenization
In: Probability theory and related fields, 178 (2020) 1/2, pp. 531-566inJournal
2020
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The structure of fluctuations in stochastic homogenization
In: Communications in mathematical physics, 377 (2020) 1, pp. 259-306inJournal
2020
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A regularity theory for random elliptic operators
In: Milan journal of mathematics, 88 (2020) 1, pp. 99-170inJournal
2020
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A variational proof of partial regularity for optimal transportation maps
In: Annales scientifiques de l'Ecole Normale Supérieure, 53 (2020) 5, pp. 1209-1233inJournal
2020
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Numerical study in stochastic homogenization for elliptic partial differential equations : convergence rate in the size of representative volume elements
In: Numerical linear algebra with applications, 27 (2020) 3, e2296inJournal
2020
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Brakke's inequality for the thresholding scheme
In: Calculus of variations and partial differential equations, 59 (2020) 1, p. 39inBook
2020
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The thresholding scheme for mean curvature flow and De Giorgi's ideas for minimizing movements
In: The role of metrics in the theory of partial differential equations : proceedings ; July 2-13, 2018 ; Hokkaido University, Sapporo / Yoshikazu Giga... (eds.)Tokyo : Mathematical Society of Japan, 2020. - pp. 63-93
(Advanced studies in pure mathematics ; 85)
inJournal
2020
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Editorial
In: Archive for rational mechanics and analysis, 235 (2020) 1, pp. 1-2inJournal
2019
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Relaxation to a planar interface in the Mullins-Sekerka problem
In: Interfaces and free boundaries, 21 (2019) 1, pp. 21-40inJournal
2019
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The magnetization ripple : a nonlocal stochastic PDE perspective
In: Journal de mathématiques pures et appliquées, 130 (2019), pp. 157-199inJournal
2019
Nucleation barriers for the cubic-to-tetragonal phase transformation in the absence of self-accommodation
In: Zeitschrift für angewandte Mathematik und Mechanik, 99 (2019) 2, e201800179inJournal
2019
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A generalization of the entropy identity for Burgers' equation and application to the Kuramoto-Sivashinsky equation [In: Mathematical aspects of hydrodynamics ; 18 August - 24 August 2019 ; report no. 38/2019]
In: Oberwolfach reports, 16 (2019) 3, pp. 2374-2377inJournal
2019
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Optimal \(L^1\)-relaxation rates for the Cahn-Hilliard equation on the line [In: Surface, bulk, and geometric partial differential equations : interfacial, stochastic, non-local and discrete structures ; 20 January - 26 January 2019 ; report no. 3/2019]
In: Oberwolfach reports, 16 (2019) 1, pp. 170-172inJournal
2019
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Optimal \(L^1\)-type relaxation rates for the Cahn-Hilliard equation on the line
In: SIAM journal on mathematical analysis, 51 (2019) 6, pp. 4645-4682inJournal
2019
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Quantitative stochastic homogenization [In: Computational multiscale methods ; 28 July - 3 August 2019 ; report no. 35/2019]
In: Oberwolfach reports, 16 (2019) 3, pp. 2160-2163inJournal
2019
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Quasi-linear SPDEs in divergence form
In: Stochastics and partial differential equations : analysis and computations, 7 (2019) 1, pp. 64-85inJournal
2019
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Quasilinear SPDEs via rough paths
In: Archive for rational mechanics and analysis, 232 (2019) 2, pp. 873-950inJournal
2018
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A Liouville theorem for elliptic systems with degenerate ergodic coefficients
In: The annals of applied probability, 28 (2018) 3, pp. 1379-1422inJournal
2018
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A branched transport limit of the Ginzburg-Landau functional
In: Journal de l'Ecole polytechnique : mathématiques, 5 (2018), pp. 317-375Preprint
2018
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The quantitative hydrodynamic limit of the Kawasaki dynamics
Preprint
2018
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Toward a quantitative theory of the hydrodynamic limit
Preprint
2018
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A large-scale regularity theory for the Monge-Ampere equation with rough data and application to the optimal matching problem
inJournal
2018
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On the regularity of weak solutions to Burgers' equation with finite entropy production
In: Calculus of variations and partial differential equations, 57 (2018) 4, p. 94inJournal
2018
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A variational approach to regularity for the Monge-Ampère equation, and an application to the matching problem [In: Calculus of variations ; 29 July - 4 August 2018 ; report no. 35/2018]
In: Oberwolfach reports, 15 (2018) 3, pp. 2121-2124inJournal
2018
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Characterizing fluctuations in stochastic homogenization [In: Interplay of analysis and probability in applied mathematics ; 11 February - 17 February 2018 ; report no. 6/2018]
In: Oberwolfach reports, 15 (2018) 1, pp. 364-367inBook
2018
Nonlinear partial differential equations and interfacial motions as gradient flow
In: The role of metrics in the theory of partial differential equations : [program and abstracts] ; July 2-13, 2018 ; Hokkaido University, Sapporo / Yoshikazu Giga... (eds.)Sapporo : Hokkaido University, 2018. - pp. 33-43
(Hokkaido University technical report series in mathematics ; 174)
Preprint
2018
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Parabolic equations with rough coefficients and singular forcing
inJournal
2018
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The impact of the SIAM Journal on Mathematical Analysis' most popular paper
In: SIAM news, 51 (2018) 5, pp. 9-9Book
2017
Mathematical thermodynamics of complex fluids : Cetraro, Italy, June 29 - July 3, 2015
Cham : Springer, 2017. - ix, 145(Lecture notes in mathematics ; 2200)
ISBN: 978-3-319-67600-5, ISBN: 978-3-319-67599-2, ISSN: 0075-8434
inBook
2017
Preface to CIME lecture notes
In: Mathematical thermodynamics of complex fluids : Cetraro, Italy, June 29 - July 3, 2015Cham : Springer, 2017. - v-vii
(Lecture notes in mathematics ; 2200)
Preprint
2017
Liouville properties and error estimates for elliptic equations in exterior domains
inBook
2017
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Quantitative stochastic homogenization : local control of homogenization error through corrector
In: Mathematics and materials / Mark J. Bowick... (eds.)Providence, RI : American mathematical society, 2017. - pp. 301-327
(IAS/Park City mathematics series ; 23)
inJournal
2017
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Stochastic homogenization of linear elliptic equations : higher-order error estimates in weak norms via second-order correctors
In: SIAM journal on mathematical analysis, 49 (2017) 6, pp. 4658-4703inJournal
2017
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Green's function for elliptic systems : existence and Delmotte-Deuschel bounds
In: Calculus of variations and partial differential equations, 56 (2017) 6, p. 163inJournal
2017
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Sublinear growth of the corrector in stochastic homogenization : optimal stochastic estimates for slowly decaying correlations
In: Stochastics and partial differential equations : analysis and computations, 5 (2017) 2, pp. 220-255inJournal
2017
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Quantitative results on the corrector equation in stochastic homogenization
In: Journal of the European Mathematical Society, 19 (2017) 11, pp. 3489-3548Preprint
2017
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A numerical primer in 2D stochastic homogenization : CLT scaling in the representative volume element
inJournal
2017
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Kornwachstum in Polykristallen: Algorithmen für den mittleren Krümmungsfluss
In: Jahrbuch der Max-Planck-Gesellschaft, 2017 (2017), Forschungsbericht - Max-Planck-Institut für Mathematik in den NaturwissenschafteninJournal
2017
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Limitations of the background field method applied to Rayleigh-Bénard convection
In: Journal of mathematical physics, 58 (2017) 9, p. 093102inJournal
2017
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Brakke - de Giorgi - Osher [In: Variational methods for evolution ; 12 November - 18 November 2017 ; report no. 54/2017]
In: Oberwolfach reports, 14 (2017) 4, pp. 3219-3222inJournal
2017
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Effective multipole expansion in random media [In: Material theories ; 16 July - 22 July 2017 ; report no. 33/2017]
In: Oberwolfach reports, 14 (2017) 3, pp. 2068-2071inJournal
2017
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Regularity for Monge-Ampère by Benamou-Brenier [In: Applications of optimal transportation in the natural sciences ; 29 January - 4 February 2017 ; report no. 7/2017]
In: Oberwolfach reports, 14 (2017) 1, pp. 345-347inBook
2017
Rigorous bounds on scaling laws in fluid dynamics
In: Mathematical thermodynamics of complex fluids : Cetraro, Italy, June 29 - July 3, 2015Cham : Springer, 2017. - pp. 101-145
(Lecture notes in mathematics ; 2200)
inJournal
2016
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Corrector estimates for elliptic systems with random periodic coefficients
In: Multiscale modeling and simulation, 14 (2016) 4, pp. 1434-1462inJournal
2016
Corrigendum to 'Smooth zero-contact-angle solutions to a thin-film equation around the steady state' (J. Differential equations 245 (2008) 1454-1506)
In: Journal of differential equations, 261 (2016) 2, pp. 1622-1635inJournal
2016
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A maximal regularity estimate for the non-stationary Stokes equation in the strip
In: Journal of differential equations, 260 (2016) 7, pp. 5589-5626inJournal
2016
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Upper bounds on Nusselt number at finite Prandtl number
In: Journal of differential equations, 260 (2016) 4, pp. 3860-3880inJournal
2016
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Interpolation inequalities in pattern formation
In: Journal of functional analysis, 271 (2016) 11, pp. 3348-3392inJournal
2016
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Branched microstructures in the Ginzburg-Landau model of type-I superconductors
In: SIAM journal on mathematical analysis, 48 (2016) 4, pp. 2994-3034inJournal
2016
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Interacting tails of asymmetric domain walls : theory and experiments
In: Physical review / B, 93 (2016) 2, p. 024414inJournal
2016
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Topology and hysteretic domain-wall transitions in ferromagnets [In: Mechanics of materials : mechanics of interfaces and evolving microstructure ; 13 March - 19 March ; report no. 17/2016]
In: Oberwolfach reports, 13 (2016) 1, pp. 817-818inJournal
2016
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A higher-order large-scale regularity theory for random elliptic operators
In: Communications in partial differential equations, 41 (2016) 7, pp. 1108-1148inJournal
2016
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Rigorous asymptotics of traveling-wave solutions to the thin-film equation and Tanner's law
In: Nonlinearity, 29 (2016) 9, pp. 2497-2536inJournal
2016
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Convergence of the thresholding scheme for multi-phase mean-curvature flow
In: Calculus of variations and partial differential equations, 55 (2016) 5, p. 129inJournal
2016
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Anchored Nash inequalities and heat kernel bounds for static and dynamic degenerate environments
In: Journal of functional analysis, 270 (2016) 1, pp. 201-228inJournal
2016
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Correlation structure of the corrector in stochastic homogenization
In: The annals of probability, 44 (2016) 5, pp. 3207-3233inJournal
2016
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The magnetization ripple revisited [In: Mini-workshop : mathematics of magnetoelastic materials ; 30 October - 5 November 2016 ; report no. 51/2016]
In: Oberwolfach reports, 13 (2016) 4, pp. 2917-2919inJournal
2015
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Threshold dynamics for networks with arbitrary surface tensions
In: Communications on pure and applied mathematics, 68 (2015) 5, pp. 808-864inJournal
2015
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Algebraic contraction rate for distance between entropy solutions of scalar conservation laws
In: Journal of mathematical analysis and applications, 435 (2015) 2, pp. 1525-1551inJournal
2015
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Quantification of ergodicity in stochastic homogenization : optimal bounds via spectral gap on Glauber dynamics
In: Inventiones mathematicae, 199 (2015) 2, pp. 455-515inJournal
2015
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Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization
In: ESAIM / Proceedings, 48 (2015), pp. 80-97Preprint
2015
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The corrector in stochastic homogenization : optimal rates, stochastic integrability, and fluctuations
inJournal
2015
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New bounds for the inhomogenous Burgers and the Kuramoto-Sivashinsky equations
In: Communications in partial differential equations, 40 (2015) 12, pp. 2237-2265inJournal
2015
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Moment bounds for the corrector in stochastic homogenization of a percolation model
In: Electronic journal of probability, 20 (2015), p. 106Preprint
2015
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An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus
inJournal
2015
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On annealed elliptic Green's function estimates
In: Mathematica bohemica, 140 (2015) 4, pp. 489-506inJournal
2015
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Quantitative stochastic homogenization of elliptic equations [In: Interplay of analysis and probability in applied mathematics ; 26 July - 1 August 2015 ; report no. 35/2015]
In: Oberwolfach reports, 12 (2015) 3, pp. 2030-2033Preprint
2015
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Hölder regularity for a non-linear parabolic equation driven by space-time white noise
inJournal
2014
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A reduced model for domain walls in soft ferromagnetic films at the cross-over from symmetric to asymmetric wall types
In: Journal of the European Mathematical Society, 16 (2014) 7, pp. 1377-1422inJournal
2014
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Well-posedness for the Navier-Slip thin-film equation in the case of complete wetting
In: Journal of differential equations, 257 (2014) 1, pp. 15-81inJournal
2014
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An optimal quantitative two-scale expansion in stochastic homogenization of discrete elliptic equations
In: ESAIM / Mathematical modelling and numerical analysis, 48 (2014) 2, pp. 325-346Preprint
2014
Quantitative theory in stochastic homogenization
inJournal
2014
Nonexistence of a minimizer for Thomas-Fermi-Dirac-von Weizsäcker model
In: Communications on pure and applied mathematics, 67 (2014) 10, pp. 1605-1617inJournal
2014
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Annealed estimates on the Green function
In: Probability theory and related fields, 163 (2014) 3-4, pp. 527-573inJournal
2014
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Effektive Beschreibung von heterogenen Medien
In: Jahrbuch der Max-Planck-Gesellschaft, 2014 (2014), Forschungsbericht - Max-Planck-Institut für Mathematik in den NaturwissenschafteninJournal
2014
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Invariant measure of the stochastic Allen-Cahn equation : the regime of small noise and large system size
In: Electronic journal of probability, 19 (2014), p. 23inJournal
2014
Relaxation to equilibrium in the one-dimensional Cahn-Hilliard equation
In: SIAM journal on mathematical analysis, 46 (2014) 1, pp. 720-756inJournal
2013
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Regularity of source-type solutions to the thin-film equation with zero contact angle and mobility exponent between 3/2 and 3
In: European journal of applied mathematics, 24 (2013) 5, pp. 735-760inJournal
2013
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Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric
In: Calculus of variations and partial differential equations, 47 (2013) 1-2, pp. 181-206inJournal
2013
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A quantitative two-scale expansion in stochastic homogenization [In: Interplay of theory and numerics for deterministic and stochastic homogenization ; 17 March - 23 March 2013 ; report no. 14/2013]
In: Oberwolfach reports, 10 (2013) 1, pp. 821-821inJournal
2013
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Nucleation barriers for the cubic-to-tetragonal phase transformation
In: Communications on pure and applied mathematics, 66 (2013) 6, pp. 867-904inJournal
2013
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Regularity for elliptic equations with i.i.d. coefficients [In: Classical and quantum mechanical models of many-particle systems ; 1 December - 7 December 2013 ; report no. 57/2013]
In: Oberwolfach reports, 10 (2013) 4, pp. 3352-3354inJournal
2013
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Uniform logarithmic Sobolev inequalities for conservative spin systems with super-quadratic single-site potential
In: The annals of probability, 41 (2013) 3B, pp. 2182-2224inJournal
2013
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A quantitative theory in stochastic homogenization [In: Interplay of theory and numerics for deterministic and stochastic homogenization ; 17 March - 23 March 2013 ; report no. 14/2013]
In: Oberwolfach reports, 10 (2013) 1, pp. 848-849inJournal
2013
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Crossover of the coarsening rates in demixing of binary viscous liquids
In: Communications in mathematical sciences, 11 (2013) 2, pp. 441-464inJournal
2013
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Optimal martensitic inclusions [In: Material theories ; 15 December - 21 December 2013 ; report no. 59/2013]
In: Oberwolfach reports, 10 (2013) 4, pp. 3443-3443inJournal
2013
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Rayleigh-Bénard convection : bounds on the Nusselt number [In: Geophysical fluid dynamics ; 17 February - 23 February 2013 ; report no. 10/2013]
In: Oberwolfach reports, 10 (2013) 1, pp. 544-545inJournal
2013
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Stability of kinks in Cahn-Hilliard equations - energy/energy dissipation methods [In: Classical and quantum mechanical models of many-particle systems ; 1 December - 7 December 2013 ; report no. 57/2013]
In: Oberwolfach reports, 10 (2013) 4, pp. 3363-3363inJournal
2012
A constrained model for MSMA
In: Advanced engineering materials, 14 (2012) 8, pp. 594-600inJournal
2012
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A quantitative rigidity result for the cubic-to-tetragonal phase transition in the geometrically linear theory with interfacial energy
In: Proceedings of the Royal Society of Edinburgh / A, 142 (2012) 2, pp. 273-327inBook
2012
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Domain configurations in soft ferromagnetic films under external field
In: Proceedings of MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling, Vienna, February 15 - 17, 2012Vienna : International Federation of Automatic Control, 2012. - pp. 498-503
inJournal
2012
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An optimal error estimate in stochastic homogenization of discrete elliptic equations
In: The annals of applied probability, 22 (2012) 1, pp. 1-28inJournal
2012
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Domain and wall pattern in ferromagnets [In: Dynamics of patterns ; 16 December - 22 December 2012 ; report no. 60/2012]
In: Oberwolfach reports, 9 (2012) 4, pp. 3620-3622inJournal
2012
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Formation and coarsening of the concertina magnetization pattern in elongated thin-film elements
In: Physical review / B, 85 (2012) 10, p. 104407inJournal
2011
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Upper bounds on coarsening rates in demixing binary viscous liquids
In: SIAM journal on mathematical analysis, 43 (2011) 1, pp. 114-134inJournal
2011
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Generalised Einstein relation for hot Brownian motion
In: epl, 96 (2011) 6, p. 60009inJournal
2011
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Domänen- und Wandmuster in ferromagnetischen Filmen
In: Jahrbuch der Max-Planck-Gesellschaft, 2011 (2011), Forschungsbericht - Max-Planck-Institut für Mathematik in den NaturwissenschafteninJournal
2011
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Threshold dynamics for arbitrary surface tensions [In: Geometric partial differential equations : theory, numerics and applications ; November 27th - December 3rd, 2011 ; report no. 54/2011]
In: Oberwolfach reports, 8 (2011) 4, pp. 3138-3140inJournal
2011
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An optimal variance estimate in stochastic homogenization of discrete elliptic equations
In: The annals of probability, 39 (2011) 3, pp. 779-856inJournal
2011
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A compactness result for Landau state in thin-film micromagnetics
In: Annales de l'Institut Henri Poincaré / C, 28 (2011) 2, pp. 247-282inJournal
2011
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Variational methods for evolution ; December 4th - December 10th, 2011 ; report no. 55/2011
In: Oberwolfach reports, 8 (2011) 4, pp. 3145-3216inJournal
2011
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Eine Fields-Medaille für Cedric Villani
In: Mitteilungen der Deutschen Mathematiker-Vereinigung, 19 (2011) 1, pp. 24-26inJournal
2011
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Rayleigh-Bénard convection : improved bounds on the Nusselt number
In: Journal of mathematical physics, 52 (2011) 8, p. 083702inJournal
2011
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On the coarsening rates in demixing binary viscous liquids [In: Variational methods for evolution ; December 4th - December 10th, 2011 ; report no. 55/2011]
In: Oberwolfach reports, 8 (2011) 4, pp. 3160-3162inJournal
2010
Phase transitions : May 30th - June 5th, 2010 ; report no. 24/2010
In: Oberwolfach reports, 7 (2010) 2, pp. 1431-1484inJournal
2010
Branching, coarsening, and interpolation estimates [In: Calculus of variations ; 18 July - 24 July, 2010 ; report no. 31/2010]
In: Oberwolfach reports, 7 (2010) 3, pp. 1833-1835inJournal
2010
Repository Open Access
Domain branching in uniaxial ferromagnets : asymptotic behavior of the energy
In: Calculus of variations and partial differential equations, 38 (2010) 1-2, pp. 135-181inJournal
2010
Logarithmic Sobolev inequality for a conservative spin system with single-site potentials of arbitrary super-quadratic growth [In: Classical and quantum mechanical models of many-particle systems ; December 5th - December 11th, 2010 ; report no. 54/2010]
In: Oberwolfach reports, 7 (2010) 4, pp. 3210-3212inJournal
2010
Repository Open Access
The concertina pattern : from micromagnetics to domain theory
In: Calculus of variations and partial differential equations, 39 (2010) 1-2, pp. 139-181inJournal
2010
Repository Open Access
Universal bounds for the Littlewood-Paley first-order moments of the 3D Navier-Stokes equations
In: Communications in mathematical physics, 300 (2010) 2, pp. 301-315inJournal
2010
Coarsening in energy-driven systems [In: Phase transitions ; May 30th - June 5th, 2010 ; report no. 24/2010]
In: Oberwolfach reports, 7 (2010) 2, pp. 1469-1471inJournal
2010
A functional analytic approach to logarithmic Sobolev inequalities and the hydrodynamic limit [In: Phase transitions ; May 30th - June 5th, 2010 ; report no. 24/2010]
In: Oberwolfach reports, 7 (2010) 2, pp. 1480-1480inJournal
2009
Uniform energy distribution for an isoperimetric problem with long-range interactions
In: Journal of the American Mathematical Society, 22 (2009) 2, pp. 569-605inJournal
2009
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A rigidity result for a perturbation of the geometrically linear three-well problem
In: Communications on pure and applied mathematics, 62 (2009) 12, pp. 1632-1669inJournal
2009
Ostwald ripening of droplets : the role of migration
In: European journal of applied mathematics, 20 (2009) 1, pp. 1-67inJournal
2009
Repository Open Access
A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit
In: Annales de l'Institut Henri Poincaré / B, 45 (2009) 2, pp. 302-351inJournal
2009
A quantitative rigity result for the cubic-to-tetragonal phase transition in the geometrically linear theory with interfacial energy [In: PDE and materials ; September 13th - September 19th, 2009 ; report no. 42/2009]
In: Oberwolfach reports, 6 (2009) 3, pp. 2391-2393inJournal
2009
Arbeitsgemeinschaft : Optimal transport and geometry ; March 29th - April 4th, 2009 ; report no. 18/2009
In: Oberwolfach reports, 6 (2009) 2, pp. 983-1018inJournal
2009
Journal Open Access
Optimal bounds on the Kuramoto-Sivashinsky equation
In: Journal of functional analysis, 257 (2009) 7, pp. 2188-2245inJournal
2009
Uniform energy distribution for a model of pattern formation [In: PDE and materials ; September 13th - September 19th, 2009 ; report no. 42/2009]
In: Oberwolfach reports, 6 (2009) 3, pp. 2397-2400Book
2008
Transport equations and multi-D hyperbolic conservation laws
Berlin : Springer, 2008. - xiv, 130(Lecture notes of the Unione Matematica Italiana ; 5)
ISBN: 978-3-540-76780-0, ISBN: 978-3-540-76781-7
inJournal
2008
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Ground state energy scaling laws during the onset and destruction of the intermediate state in a type I superconductor
In: Communications on pure and applied mathematics, 61 (2008) 5, pp. 595-626inBook
2008
Regularizing effect of nonlinearity in multidimensional scalar conservation laws
In: Transport equations and multi-D hyperbolic conservation laws / Luigi Ambrosio... (eds.)Berlin : Springer, 2008. - pp. 77-128
(Lecture notes of the Unione Matematica Italiana ; 5)
inBook
2008
Micro structures in thin coating layers : micro structure evolution and macroscopic contact angle
In: Mathematics - key technology for the future : joint projects between universities and industry, 2004 - 2007 / Willi Jäger... (eds.)Berlin [u. a.] : Springer, 2008. - pp. 75-97
inJournal
2008
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Smooth zero-contact-angle solutions to a thin-film equation around the steady state
In: Journal of differential equations, 245 (2008) 6, pp. 1454-1506inBook
2008
Numerical methods for the simulation of epitaxial growth and their application in the study of a meander instability
In: Mathematics - key technology for the future : joint projects between universities and industry, 2004 - 2007 / Willi Jäger... (eds.)Berlin [u. a.] : Springer, 2008. - pp. 53-73
inBook
2008
Suspensions of rod-like molecules : a FV-ELLAM-type discretization of the Smoluchowski equation describing the orientation of rod-like molecules
In: Finite volumes for complex applications V : proceedings of the 5th International Symposium held in Aussois, June 2008 / Robert Eymard... (eds.)London : ISTE, 2008. - pp. 495-502
inJournal
2008
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A compactness result in thin-film micromagnetics and the optimality of the Néel wall
In: Journal of the European Mathematical Society, 10 (2008) 4, pp. 909-956inJournal
2008
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Continuity of velocity gradients in suspensions of rod-like molecules
In: Communications in mathematical physics, 277 (2008) 3, pp. 729-758inJournal
2008
Pattern formation and partial differential equations [In: Dynamics of patterns ; December 14th - December 20th, 2008 ; report no. 57/2008]
In: Oberwolfach reports, 5 (2008) 4, pp. 3259-3261inJournal
2008
Computation of free energy differences [In: Atomistic models of materials : mathematical challenges ; April 27th - May 3rd, 2008 ; report no. 21/2008]
In: Oberwolfach reports, 5 (2008) 2, pp. 1087-1088inJournal
2007
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The concertina pattern : a bifurcation in ferromagnetic thin films
In: Journal of nonlinear science, 17 (2007) 3, pp. 221-281inJournal
2007
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Wave-type dynamics in ferromagnetic thin films and the motion of Néel walls
In: Nonlinearity, 20 (2007) 11, pp. 2519-2537inJournal
2007
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A new model for contact angle hysteresis
In: Networks and heterogeneous media, 2 (2007) 2, pp. 211-225inJournal
2007
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Action minimization and sharp-interface limits for the stochastic Allen-Cahn equation
In: Communications on pure and applied mathematics, 60 (2007) 3, pp. 393-438Preprint
2007
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Long-time convergence of an adaptive biasing force method
inJournal
2007
Magnetic domain wall motion [In: Phase transitions ; June 3rd - June 9th, 2007 ; report no. 28/2007]
In: Oberwolfach reports, 4 (2007) 2, pp. 1614-1616inJournal
2007
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A new criterion for the logarithmic Sobolev inequality and two applications
In: Journal of functional analysis, 243 (2007) 1, pp. 121-157inJournal
2007
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Slow motion of gradient flows
In: Journal of differential equations, 237 (2007) 2, pp. 372-420inJournal
2007
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On the scaling behaviour of cross-tie domain wall structures in patterned NiFe elements
In: epl, 80 (2007) 5, p. 57003inJournal
2006
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Critical fields in ferromagnetic thin films : identification of four regimes
In: Journal of nonlinear science, 16 (2006) 4, pp. 351-383inJournal
2006
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Oscillatory buckling mode in thin-film nucleation
In: Journal of nonlinear science, 16 (2006) 4, pp. 385-413inJournal
2006
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Coarsening rates in off-critical mixtures
In: SIAM journal on mathematical analysis, 37 (2006) 6, pp. 1732-1741inJournal
2006
Energy scaling and domain branching in type-I superconductors [In: PDE and materials ; September 24th - September 30th, 2006 ; report no. 44/2006]
In: Oberwolfach reports, 3 (2006) 4, pp. 2644-2647inJournal
2006
Nonuniversality in low-volume-fraction Ostwald ripening
In: Journal of statistical physics, 124 (2006) 1, pp. 231-259inJournal
2006
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2-d stability of the Néel wall
In: Calculus of variations and partial differential equations, 27 (2006) 2, pp. 233-253inBook
2006
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Recent analytical developments in micromagnetics
In: The science of hysteresis. Vol. 2 Physical modeling, micromagnetics, and magnetization dynamics / Giogio Bertotti... (eds.)Amsterdam : Elsevier [u. a.], 2006. - pp. 269-381
inJournal
2006
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Bounds on vertical heat transport for infinite-Prandtl-number Raleigh-Bénard convection
In: Journal of fluid mechanics, 560 (2006), pp. 229-241inJournal
2006
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Multiscale simulations for suspensions of rod-like molecules
In: Journal of computational physics, 216 (2006) 1, pp. 52-75inJournal
2006
Long-time asymptotics of a multiscale model for polymeric fluid flows
In: Archive for rational mechanics and analysis, 181 (2006) 1, pp. 97-148inJournal
2006
2-d stability of the Néel wall [In: Calculus of variations ; July 9th - July 15th, 2006 ; report no. 31/2006]
In: Oberwolfach reports, 3 (2006) 3, pp. 1928-1930inJournal
2006
Diffusive slowdown in miscible viscous fingering
In: Communications in mathematical sciences, 4 (2006) 1, pp. 267-273inBook
2006
On the effect of correlations, fluctuations and collisions in Ostwald ripening
In: Analysis, modeling and simulation of multiscale problems / Alexander Mielke (ed.)Berlin [u.a.] : Springer, 2006. - pp. 501-530
inJournal
2006
Coarsening rates for a droplet model : rigorous upper bounds
In: SIAM journal on mathematical analysis, 38 (2006) 2, pp. 503-529inJournal
2006
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Eulerian calculus for the contraction in the Wasserstein distance
In: SIAM journal on mathematical analysis, 37 (2006) 4, pp. 1227-1255inJournal
2006
Pattern formation in micromagnetics [In: Calculus of variations ; July 9th - July 15th, 2006 ; report no. 31/2006]
In: Oberwolfach reports, 3 (2006) 3, pp. 1910-1910inJournal
2005
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New bounds for the Kuramoto-Sivashinsky equation
In: Communications on pure and applied mathematics, 58 (2005) 3, pp. 297-318inJournal
2005
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On first-order corrections to the LSW theory. Pt. 1 Infinite systems
In: Journal of statistical physics, 119 (2005) 1/2, pp. 61-122inJournal
2005
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On first-order corrections to the LSW theory. Pt. 2 Finite systems
In: Journal of statistical physics, 119 (2005) 1/2, pp. 123-164inJournal
2005
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Dynamic scaling in miscible viscous fingering
In: Communications in mathematical physics, 257 (2005) 2, pp. 303-317inJournal
2005
A non-equilibrium statistical mechanics approach to effective theories of domain coarsening [In: Reactive flow and transport through complex systems ; Oktober 30th - November 5th, 2005 ; report no. 49/2005]
In: Oberwolfach reports, 2 (2005) 4, pp. 2812-2813inJournal
2005
Convergence of thin film approximation for a scalar conservation law
In: Journal of hyperbolic differential equations, 2 (2005) 1, pp. 183-199inBook
2005
Discretisation and numerical tests of a diffuse-interface model with Ehrlich-Schwoebel barrier
In: Multiscale modeling in epitaxial growth : mini-workshop at Mathematisches Forschungsinstitut Oberwolfach, January 18 - 24, 2004 / Axel Voigt (ed.)Basel [u. a.] : Birkhäuser, 2005. - pp. 127-158
(International series of numerical mathematics ; 149)
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2004
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Energy minimization and flux domain structure in the intermediate state of a type-I superconductor
In: Journal of nonlinear science, 14 (2004) 2, pp. 119-171inJournal
2004
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Minimal entropy conditions for Burgers equation
In: Quarterly of applied mathematics, 62 (2004) 4, pp. 687-700inJournal
2004
Minimal entropy conditions for Burgers equation [In: Hyperbolic conservation laws ; April 4th - April 10th, 2004 ; report no. 18/2004]
In: Oberwolfach reports, 1 (2004) 2, pp. 925-925Preprint
2004
Maximal regularity for a degenerate operator of fourth order
inBook
2004
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A reduced model for simulating grain growth
In: Free boundary problems : theory and applications / Pierluigi Colli... (eds.)Basel [u. a.] : Birkhäuser, 2004. - pp. 177-187
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2004
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Identification of the dilute regime in particle sedimentation
In: Communications in mathematical physics, 250 (2004) 2, pp. 415-432inJournal
2004
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A phenomenological model for hysteresis in polycrystalline shape memory alloys
In: Zeitschrift für angewandte Mathematik und Mechanik, 84 (2004) 12, pp. 835-842inJournal
2004
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A diffuse-interface approximation for step flow in epitaxial growth
In: Nonlinearity, 17 (2004) 2, pp. 477-491inJournal
2004
Structure of entropy solutions [In: Hyperbolic conservation laws ; April 4th - April 10th, 2004 ; report no. 18/2004]
In: Oberwolfach reports, 1 (2004) 2, pp. 929-929inJournal
2004
Upper bounds on coarsening rates [In: Mini-workshop : multiscale modeling in epitaxial growth ; January 18th - January 24th, 2004 ; report no. 4/2004]
In: Oberwolfach reports, 1 (2004) 1, pp. 234-235inJournal
2004
Discretization and numerical tests of a diffuse-interface model with Ehrlich-Schwoebel barrier [In: Mini-workshop : multiscale modeling in epitaxial growth ; January 18th - January 24th, 2004 ; report no. 4/2004]
In: Oberwolfach reports, 1 (2004) 1, pp. 235-235inBook
2003
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Multiscale modeling of materials : the role of analysis
In: Trends in nonlinear analysis / Markus Kirkilionis... (eds.)Berlin [u. a.] : Springer, 2003. - pp. 375-408
inJournal
2003
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Structure of entropy solutions for multi-dimensional scalar conservation laws
In: Archive for rational mechanics and analysis, 170 (2003) 2, pp. 137-184inJournal
2003
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Structure of entropy solutions to the eikonal equation
In: Journal of the European Mathematical Society, 5 (2003) 2, pp. 107-145inJournal
2003
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Repulsive interaction of Néel walls, and the internal length scale of the cross-tie wall
In: Multiscale modeling and simulation, 1 (2003) 1, pp. 57-104inJournal
2003
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Rigorous lubrication approximation
In: Interfaces and free boundaries, 5 (2003) 4, pp. 483-529inJournal
2003
Excitations in thin film ferromagnetic elements [In: PDE and materials ; September 7th - September 13th, 2003 ; report no. 39/2003]
In: Oberwolfach reports, 2003 (2003) 39, pp. 3-3inJournal
2003
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Coarsening dynamics for the convective Cahn-Hilliard equation
In: Physica / D, 178 (2003) 3-4, pp. 127-148inJournal
2002
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A reduced theory for thin-film micromagnetics
In: Communications on pure and applied mathematics, 55 (2002) 11, pp. 1408-1460inJournal
2002
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Low energy domain patterns in soft ferromagnetic films
In: Journal of magnetism and magnetic materials, 242-245 (2002) 2, pp. 1047-1051inJournal
2002
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Droplet spreading : intermediate scaling law by PDE methods
In: Communications on pure and applied mathematics, 55 (2002) 2, pp. 217-254inJournal
2002
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Line-energy Ginzburg-Landau models : zero-energy states
In: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 1 (2002) 2, pp. 187-202inJournal
2002
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Upper bounds on coarsening rates
In: Communications in mathematical physics, 229 (2002) 3, pp. 375-395inBook
2002
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Cross-over in scaling laws : a simple example from micromagnetics
In: Proceedings of the International Congress of Mathematicians : Beijing, 2002, August 20 - 28. Pt. 3 Invited lectures / Li Tatsien (ed.)Beijing : Higher Education Press, 2002. - pp. 829-838
inJournal
2002
Structure of entropy solutions [In: Calculus of variations ; June 30th - July 6th, 2002 ; report no. 33/2002]
In: Oberwolfach reports, 2002 (2002) 33, pp. 8-8inJournal
2001
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A compactness result in the gradient theory of phase transitions
In: Proceedings of the Royal Society of Edinburgh / A, 131 (2001) 4, pp. 833-844inJournal
2001
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Two-dimensional modelling of soft ferromagnetic films
In: Proceedings of the Royal Society of London / A, 457 (2001) 2016, pp. 2983-2991inJournal
2001
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Variational formulation for the lubrication approximation of the Hele-Shaw flow
In: Calculus of variations and partial differential equations, 13 (2001) 3, pp. 377-403inJournal
2001
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Domain coarsening in thin films
In: Communications on pure and applied mathematics, 54 (2001) 3, pp. 361-384inJournal
2001
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Ostwald ripening : the screening length revisited
In: Calculus of variations and partial differential equations, 13 (2001) 1, pp. 33-68inJournal
2001
Comment on 'Hypercontractivity of Hamilton-Jacobi equations', by S. Bobkov, I. Gentil and M. Ledoux [J. Math. Pures Appl. (9) 80 (2001), no. 7, 669-696]
In: Journal de mathématiques pures et appliquées, 80 (2001) 7, pp. 697-700inBook
2001
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Evolution of microstructure : an example
In: Ergodic theory, analysis, and efficient simulation of dynamical systems / Bernd Fiedler (ed.)Berlin [u. a.] : Springer, 2001. - pp. 501-522
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2001
Scaling laws for the cross-tie wall [In: Partial differential equations ; August 5th - August 11th, 2001 ; report no. 35/2001]
In: Oberwolfach reports, 2001 (2001) 35, pp. 8-8inJournal
2001
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The geometry of dissipative evolution equations: the porous medium equation
In: Communications in partial differential equations, 26 (2001) 1-2, pp. 101-174inBook
2000
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Magnetic microstructures : a paradigm of multiscale problems
In: ICIAM 99 : proceedings of the Fourth International Congress on Industrial and Applied Mathematics, Edinburgh / John M. Ball... (eds.)Oxford : Oxford University Press, 2000. - pp. 175-190
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2000
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Solute transport in porous media with equilibrium and nonequilibrium multiple-site adsorption : uniqueness of weak solutions
In: Nonlinear analysis / A, 42 (2000) 3, pp. 381-403inJournal
2000
Evolution of microstructure in two-phase flow [In: The mathematics of porous media = Mathematik poröser Medien ; 23.01. - 29.01.2000 ; report no. 04/2000]
In: Oberwolfach reports, 2000 (2000) 4, pp. 6-6inJournal
2000
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Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
In: Journal of functional analysis, 173 (2000) 2, pp. 361-400inJournal
2000
Thin viscous films [In: Mathematical continuum mechanics ; 20.08. - 26.08.2000 ; report no. 34/2000]
In: Oberwolfach reports, 2000 (2000) 34, pp. 9-10inJournal
1999
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Domain branching in uniaxial ferromagnets : a scaling law for the minimum energy
In: Communications in mathematical physics, 201 (1999) 1, pp. 61-79inJournal
1999
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Evolution of microstructure in unstable porous media flow : a relaxational approach
In: Communications on pure and applied mathematics, 52 (1999) 7, pp. 873-915inJournal
1999
The geometry of dissipative evolution equations : the porous medium equation [In: Partial differential equations ; 13.06. - 19.06.1999 ; Tagungsbericht 26/1999]
In: Oberwolfach reports, 1999 (1999) 24, pp. 7-7inJournal
1998
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The variational formulation of the Fokker-Planck equation
In: SIAM journal on mathematical analysis, 29 (1998) 1, pp. 1-17inJournal
1998
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A regularizing effect of nonlinear transport equations
In: Quarterly of applied mathematics, 56 (1998) 2, pp. 355-375inJournal
1998
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Dynamics of labyrinthine pattern formation in magnetic fluids : a mean-field theory
In: Archive for rational mechanics and analysis, 141 (1998) 1, pp. 63-103inJournal
1998
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Lubrication approximation with prescribed nonzero contact angle
In: Communications in partial differential equations, 23 (1998) 11/12, pp. 2077-2164inJournal
1997
Free energy and the Fokker-Planck equation
In: Physica / D, 107 (1997) 2-4, pp. 265-271inBook
1997
Remarks about metastability
In: Computational science for the 21st century : dedicated to Prof. Roland Glowinski on the occasion of his 60th birthday ; symposium, tours, France, May 5-7, 1997 / Marie Odile Bristeau (ed.)Chichester : Wiley, 1997. - pp. 3-12
inBook
1997
The route to stability through Fokker-Planck dynamics
In: Differential equations and applications : proceedings of the US-Chinese conference, held in Hangzhou, June 24 - 29, 1996 / edited by P. W. Bates ... / P. W. Bates (ed.)Boston [u. a.] : International Press, 1997. - pp. 108-126
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1997
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Small surface energy, coarse-graining, and selection of microstructure
In: Physica / D, 107 (1997) 2-4, pp. 272-289inJournal
1997
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L1-contraction and uniqueness for unstationary saturated-unsaturated porous media flow
In: Advances in mathematical sciences and applications, 7 (1997) 2, pp. 537-553inJournal
1997
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Thermodynamically driven incompressible fluid mixtures
In: The journal of chemical physics, 107 (1997) 23, pp. 10177-10184inJournal
1997
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Viscous fingering : an optimal bound on the growth rate of the mixing zone
In: SIAM journal on applied mathematics, 57 (1997) 4, pp. 982-990inBook
1996
Scalar conservation laws
In: Weak and measure-valued solutions to evolutionary PDEs / Josef Málek... (eds.)London : Chapman and Hall/CRS, 1996. - pp. 41-143
(Applied mathematics and mathematical computation ; 13)
Preprint
1996
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Doubly degenerate diffusion equations as steepest descent
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1996
Initial-boundary value problem for a scalar conservation law
In: Comptes rendus de l'Académie des Sciences / 1, 322 (1996) 8, pp. 729-734inJournal
1996
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L1-contraction and uniqueness for quasilinear elliptic-parabolic equations
In: Journal of differential equations, 131 (1996) 1, pp. 20-38inJournal
1995
L1-contraction and uniqueness for quasilinear elliptic-parabolic equations
In: Comptes rendus de l'Académie des Sciences / 1, 321 (1995) 8, pp. 1005-1010Preprint
1994
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Stability investigation of planar solutions of the Buckley-Leverett equations
Academic
1992
Ein Randwertproblem für skalare Erhaltungssätze
Dissertation, Universität Bonn, 1992Open Access Types
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