Research Group
Pattern Formation, Energy Landscapes and Scaling Laws - Publications
Explore the scholarly works of the "Pattern Formation, Energy Landscapes and Scaling Laws" group. Browse journal articles, contributions in books and conference proceedings, academic theses, or discover our latest research through preprints.
inJournal
2024
Repository Open Access
A hidden convexity in continuum mechanics, with application to classical, continuous-time, rate-(in)dependent plasticity
In: Mathematics and mechanics of solids, (2024)inJournal
2024
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Approximations of dispersive PDEs in the presence of low-regularity randomness
In: Foundations of computational mathematics, (2024)inJournal
2024
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Hairer's multilevel Schauder estimates without regularity structures
In: Transactions of the American Mathematical Society, (2024)Preprint
2024
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Lecture notes on Malliavin calculus in regularity structures
inJournal
2024
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Convergence of space-discretised gKPZ via regularity structures
In: The annals of applied probability, 34 (2024) 2, pp. 2488-2538inJournal
2024
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Diagram-free approach for convergence of tree-based models in regularity structures
In: Journal of the Mathematical Society of Japan, (2024)inJournal
2024
Repository Open Access
A free discontinuity approach to optimal profiles in Stokes flows
In: Annales de l'Institut Henri Poincaré / C, (2024)inJournal
2024
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Annealed quantitative estimates for the quadratic 2D-discrete random matching problem
In: Probability theory and related fields, 190 (2024) 1/2, pp. 485-541inJournal
2024
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Bias in the representative volume element method : periodize the ensemble instead of its realizations
In: Foundations of computational mathematics, 24 (2024) 4, pp. 1305-1387inJournal
2024
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On a novel gradient flow structure for the aggregation equation
In: Calculus of variations and partial differential equations, 63 (2024) 5, p. 126inJournal
2024
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There is no stationary \(p\)-cyclically monotone Poisson matching in 2D
In: Electronic journal of probability, 29 (2024), p. 106inJournal
2024
Repository Open Access
Stochastic homogenization and geometric singularities : a study on corners
In: SIAM journal on mathematical analysis, 56 (2024) 2, pp. 2395-2455inJournal
2024
Repository Open Access
Gradient estimates, Bakry-Emery Ricci curvature and ellipticity for unbounded graph Laplacians
In: Communications in analysis and geometry, 32 (2024) 2, pp. 343-364inJournal
2024
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Geometric linearisation for optimal transport with strongly p-convex cost
In: Calculus of variations and partial differential equations, 63 (2024) 4, p. 87inJournal
2024
Journal Open Access
Quantified legendreness and the regularity of minima
In: Archive for rational mechanics and analysis, 248 (2024) 4, p. 69Preprint
2024
Repository Open Access
Time-dependent averages of a critical long-range stochastic heat equation
Preprint
2024
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Median filter method for mean curvature flow using a random Jacobi algorithm
inJournal
2024
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A diagram-free approach to the stochastic estimates in regularity structures
In: Inventiones mathematicae, 237 (2024) 3, pp. 1469-1565inJournal
2024
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Optimal artificial boundary conditions based on second-order correctors for three dimensional random elliptic media
In: Communications in partial differential equations, 49 (2024) 7/8, pp. 609-670Academic
2024
A variational approach to the optimal matching problem
Dissertation, Universität Münster, 2024Preprint
2024
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Comparison principles for the Finsler infinity Laplacian with applications to minimal Lipschitz extensions
inJournal
2024
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Convergence to the planar interface for a nonlocal free-boundary evolution
In: Communications on pure and applied mathematics, (2024)inJournal
2024
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Distributional celestial amplitudes
In: Journal of high energy physics, 2024 (2024) 7, p. 120inJournal
2024
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Invariant Gibbs dynamics for the two-dimensional Zakharov-Yukawa system
In: Journal of functional analysis, 286 (2024) 4, p. 110244inJournal
2024
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Generic level sets in mean curvature flow are BV solutions
In: The journal of geometric analysis, 34 (2024) 12, p. 375inJournal
2023
Repository Open Access
Monge-Ampère gravitation as a \(\Gamma\)-limit of good rate functions
In: Analysis and PDE, 16 (2023) 9, pp. 2005-2040inJournal
2023
Journal Open Access
An example of singular elliptic stochastic PDE
In: Matemática contemporÒanea, 58 (2023), pp. 3-67Preprint
2023
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Composition and substitution of regularity structures B-series
inJournal
2023
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Post-Lie algebras in regularity structures
In: Forum of mathematics / Sigma, 11 (2023), e98inJournal
2023
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Locality properties of standard homogenization commutator
In: Asymptotic analysis, 132 (2023) 3/4, pp. 409-426Preprint
2023
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Artificial boundary conditions for random ellitpic systems with correlated coefficient field
inJournal
2023
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Well-posedness of the Kolmogorov two-equation model of turbulence in optimal Sobolev spaces
In: Journal of evolution equations, 23 (2023) 4, p. 68inJournal
2023
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The occurrence of surface tension gradient discontinuities and zero mobility for Allen-Cahn and curvature flows in periodic media
In: Interfaces and free boundaries, 25 (2023) 4, pp. 567-631inJournal
2023
Journal Open Access
A note on improved differentiability for the Banach-space valued Finsler \(\mathscr {y}\)-Laplacian
In: Comptes rendus mathematique, 361 (2023), pp. 1091-1105Preprint
2023
Repository Open Access
Almost sharp rates of convergence for the average cost and displacement in the optimal matching problem
inJournal
2023
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Nonlinear open mapping principles, with applications to the Jacobian equation and other scale-invariant PDEs
In: Advances in mathematics, 415 (2023), p. 108869inJournal
2023
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Endpoint \(L^1\) estimates for Hodge systems
In: Mathematische Annalen, 385 (2023) 3/4, pp. 1923-1946inJournal
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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Wasserstein asymptotics for the empirical measure of fractional Brownian motion on a flat torus
In: Stochastic processes and their applications, 155 (2023), pp. 1-26inJournal
2023
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Boundary regularity results for minimisers of convex functionals with \((p,q)\)-growth
In: Advances in nonlinear analysis, 12 (2023) 1, p. 20230110inJournal
2023
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Stochastic homogenization : a short proof of the annealed Calderón-Zygmund estimate
In: Journal of elliptic and parabolic equations, 9 (2023) 1, pp. 125-154Preprint
2023
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Lecture notes on the harmonic approximation to quadratic optimal transport
inJournal
2023
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Birth-death dynamics for sampling : global convergence, approximations and their asymptotics
In: Nonlinearity, 36 (2023) 11, p. 5731inJournal
2023
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Comparison principles for second-order elliptic/parabolic equations with discontinuities in the gradient compatible with Finsler norms
In: Journal of functional analysis, 285 (2023) 4, p. 109983inJournal
2023
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Transverse domain walls in thin ferromagnetic strips
In: Archive for rational mechanics and analysis, 247 (2023) 3, p. 59inJournal
2023
Journal Open Access
Quantitative heat-kernel estimates for diffusions with distributional drift
In: Potential analysis, 59 (2023) 2, pp. 731-752inJournal
2023
Journal Open Access
A trace inequality for solenoidal charges
In: Potential analysis, 59 (2023) 4, pp. 2093-2104Preprint
2022
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Low regularity integrators via decorated trees
Preprint
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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Symmetry properties of minimizers of a perturbed Dirichlet energy with a boundary penalization
In: SIAM journal on mathematical analysis, 54 (2022) 3, pp. 3636-3653Preprint
2022
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Renormalization of singular elliptic stochastic PDEs using flow equation
inJournal
2022
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Quasiconvexity, null Lagrangians, and Hardy space integrability under constant rank constraints
In: Archive for rational mechanics and analysis, 245 (2022) 1, pp. 279-320inJournal
2022
Journal Open Access
A note on a rigidity estimate for degree \(\pm 1\) conformal maps on \(\mathbb{S}^2\)
In: The bulletin of the London Mathematical Society, 54 (2022) 1, pp. 256-263inJournal
2022
Repository Open Access
The annealed Calderon-Zygmund estimate as convenient tool in quantitative stochastic homogenization
In: Journal of functional analysis, 283 (2022) 7, p. 109594inJournal
2022
Journal Open Access
Global higher integrability for minimisers of convex obstacle problems with (p,q)-growth
In: Calculus of variations and partial differential equations, 61 (2022) 3, p. 88Preprint
2022
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On global absence of Lavrentiev gap for functionals with (p,q)-growth
Preprint
2022
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On the validity of the Euler-Lagrange system without growth assumptions
inJournal
2022
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Regularity for quasilinear vectorial elliptic systems via an iterative scheme with numerical applications
In: Nonlinear differential equations and applications, 29 (2022) 6, p. 75inJournal
2022
Repository Open Access
Longtime asymptotics of the two-dimensional parabolic Anderson model with white-noise potential
In: Annales de l'Institut Henri Poincaré / B, 58 (2022) 3, pp. 1351-1384inJournal
2022
Journal Open Access
Oscillation and concentration in sequences of PDE constrained measures
In: Archive for rational mechanics and analysis, 246 (2022) 2/3, pp. 823-875Academic
2022
Repository Open Access
Effective properties of random media : expansions in dilute regimes
Dissertation, Sorbonne Université Laboratoire Jacques-Louis Lions, 2022Preprint
2022
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Focusing Gibbs measures with harmonic potential
Academic
2022
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BPX-Type preconditioners and convergence estimates for strictly quasiconvex functionals
Dissertation, Universität Leipzig, 2022inJournal
2021
Repository Open Access
\(\Gamma\)-convergence for a class of action functionals induced by gradients of convex functions
In: Rendiconti lincei : matematica e applicazioni, serie 9, 32 (2021) 1, pp. 97-108Academic
2021
Repository Open Access
Quantitative estimates in stochastic homogenization of elliptic equations and systems
Dissertation, Sorbonne Université Laboratoire Jacques-Louis Lions, 2021inJournal
2021
Journal Open Access
Echo chains as a linear mechanism : norm inflation, modified exponents and asymptotics
In: Archive for rational mechanics and analysis, 242 (2021) 1, pp. 643-700inJournal
2021
Repository Open Access
Additive functionals as rough paths
In: The annals of probability, 49 (2021) 3, pp. 1450-1479Preprint
2021
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On symmetry of energy minimizing harmonic-type maps on cylindrical surfaces
Preprint
2021
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Flow equation approach to singular stochastic PDEs
inJournal
2021
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Infrared problem in perturbative quantum field theory
In: Reviews in mathematical physics, 33 (2021) 10, p. 2150032inJournal
2021
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On limiting trace inequalities for vectorial differential operators
In: Indiana University mathematics journal, 70 (2021) 5, pp. 2133-2176inJournal
2021
Repository Open Access
Quantitative linearization results for the Monge-Ampère equation
In: Communications on pure and applied mathematics, 74 (2021) 12, pp. 2483-2560inJournal
2021
Repository Open Access
Optimal artificial boundary condition for random elliptic media
In: Foundations of computational mathematics, 21 (2021) 6, pp. 1643-1702inJournal
2021
Repository Open Access
Pointwise differentiability of higher-order for distributions
In: Analysis and PDE, 14 (2021) 2, pp. 323-354inJournal
2021
Repository Open Access
Sharp boundary \(\varepsilon\)-regularity of optimal transport maps
In: Advances in mathematics, 381 (2021), p. 107603Preprint
2021
Repository Open Access
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
2021
Repository Open Access
A rough super-Brownian motion
In: The annals of probability, 49 (2021) 2, pp. 908-943Academic
2021
Repository Open Access
Contributions au problème du transport optimal et à sa régularité
Dissertation, Université de Toulouse, 2021Academic
2021
Repository Open Access
Quantitative analysis in stochastic homogenization and hypocoercive PDEs in sampling
Dissertation, Duke University, 2021Preprint
2020
Repository Open Access
Minimizing relative entropy of path measures under marginal constraints
inJournal
2020
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Nonlinear instability in Vlasov type equations around rough velocity profiles
In: Annales de l'Institut Henri Poincaré / C, 37 (2020) 3, pp. 489-547inJournal
2020
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On the existence of a scalar pressure field in the Brödinger problem
In: SIAM journal on mathematical analysis, 52 (2020) 1, pp. 370-401Preprint
2020
Repository Open Access
Vanishing viscosity limit for viscous Burgers-Vlasov equations
inJournal
2020
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On the smallness condition in linear inviscid damping : monotonicity and resonance chains
In: Nonlinearity, 33 (2020) 11, pp. 6176-6194inJournal
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
Repository Open Access
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
Repository Open Access
Self-similar minimizers of a branched transport functional
In: Indiana University mathematics journal, 69 (2020) 4, pp. 1073-1104inJournal
2020
Journal Open Access
The infinitesimal generator of the stochastic Burgers equation
In: Probability theory and related fields, 178 (2020) 3/4, pp. 1067-1124inJournal
2020
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On the necessity of the constant rank condition for \(L^p\) estimates
In: Comptes rendus mathematique, 358 (2020) 9/10, pp. 1091-1095Preprint
2020
Repository Open Access
An introduction to generalized Young measures
inJournal
2020
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A Littlewood-Paley description of modelled distributions
In: Journal of functional analysis, 279 (2020) 6, p. 108634inJournal
2020
Repository Open Access
Elastic curves and phase transitions
In: Mathematische Annalen, 376 (2020) 3/4, pp. 1629-1674inJournal
2020
Journal Open Access
Editorial
In: Archive for rational mechanics and analysis, 235 (2020) 1, pp. 1-2inJournal
2020
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Continuity and canceling operators of order \(n\) on \({\mathbb{R}}^n\)
In: Calculus of variations and partial differential equations, 59 (2020) 2, p. 85inJournal
2020
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Nonlinear mechanics of thermoelastic accretion
In: Zeitschrift für Angewandte Mathematik und Physik, 71 (2020) 3, p. 87inJournal
2019
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The semi-global isometric embedding of surfaces with curvature changing signs stably
In: Proceedings of the American Mathematical Society, 147 (2019) 10, pp. 4343-4353inJournal
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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Pathwise integration and change of variable formulas for continuous paths with arbitrary regularity
In: Transactions of the American Mathematical Society / B, 6 (2019), pp. 161-186inJournal
2019
Repository Open Access
Exact periodic stripes for a minimizers of a local/non-local interaction functional in general dimension
In: Archive for rational mechanics and analysis, 231 (2019) 1, pp. 519-589inJournal
2019
Repository Open Access
On the exit time and stochastic homogenization of isotropic diffusions in large domains
In: Annales de l'Institut Henri Poincaré / B, 55 (2019) 2, pp. 720-755inJournal
2019
Repository Open Access
Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with \(L^p\) data
In: Journal of differential equations, 266 (2019) 1, pp. 257-311inJournal
2019
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On the optimality of stripes in a variational model with non-local interactions
In: Calculus of variations and partial differential equations, 58 (2019) 3, p. 103inJournal
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
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Decomposition and pointwise estimates of periodic Green functions of some elliptic equations with periodic oscillatory coefficients
In: Asymptotic analysis, 112 (2019) 3-4, pp. 227-246inJournal
2019
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Some quantitative homogenization results in a simple case of interface
In: Communications in partial differential equations, 44 (2019) 10, pp. 907-939inJournal
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
Journal Open Access
On time-periodic solutions to parabolic boundary value problems
In: Mathematische Annalen, 374 (2019) 1-2, pp. 37-65inJournal
2019
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Paracontrolled distributions on Bravais lattices and weak universality of the 2d parabolic Anderson model
In: Annales de l'Institut Henri Poincaré / B, 55 (2019) 4, pp. 2058-2110inJournal
2019
Repository Open Access
Pointwise differentiability of higher order for sets
In: Annals of global analysis and geometry, 55 (2019) 3, pp. 591-621inJournal
2019
Repository Open Access
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
Repository Open Access
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
Repository Open Access
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
Repository Open Access
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
Journal Open Access
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
2019
Journal Open Access
The KPZ equation on the real line
In: Electronic journal of probability, 24 (2019), p. 117inJournal
2019
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A note on estimates for elliptic systems with \(L^1\) data
In: Comptes rendus mathematique, 357 (2019) 11/12, pp. 851-857inJournal
2019
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On the forced Euler and Navier-Stokes equations : linear damping and modified scattering
In: Journal of mathematical fluid mechanics, 21 (2019) 4, p. 49inJournal
2018
Journal Open Access
A branched transport limit of the Ginzburg-Landau functional
In: Journal de l'Ecole polytechnique : mathématiques, 5 (2018), pp. 317-375inJournal
2018
Repository Open Access
On the convergence of minimizers of singular perturbation functionals
In: Indiana University mathematics journal, 67 (2018) 4, pp. 1665-1682inJournal
2018
Pattern formation for a family of models with local/nonlocal interactions
In: Proceedings in applied mathematics and mechanics, 18 (2018) 1, e201800352Preprint
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
inJournal
2018
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Threshold dynamics for anisotropic surface energies
In: Mathematics of computation, 87 (2018) 312, pp. 1721-1756inJournal
2018
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Strong stability of 2D viscoelastic Poiseuille-type flows
In: Advances in mathematical sciences and applications, 27 (2018) 1, pp. 143-167Preprint
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
Repository Open Access
Spatially discrete reaction-diffusion equations with discontinuous hysteresis
In: Annales de l'Institut Henri Poincaré / C, 35 (2018) 4, pp. 1041-1077inJournal
2018
Repository Open Access
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
Repository Open Access
An isoperimetric inequality for diffused surfaces
In: Kodai mathematical journal, 41 (2018) 1, pp. 70-85inBook
2018
Lagrangian representation for systems of conservation laws : an overview
In: Theory, numerics and applications of hyperbolic problems II : Aachen, Germany, August 2016 / Christian Klingenberg... (eds.)Cham : Springer, 2018. - pp. 335-347
(Springer proceedings in mathematics and statistics ; 237)
inJournal
2018
Repository Open Access
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
Repository Open Access
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. 9-9inJournal
2018
Repository Open Access
On the pattern formation for a family of functionals with short-range/long-range interactions in competition [In: Emergence of structures in particle systems : mechanics, analysis and computation ; 28 October - 3 November 2018 ; report no. 49/2018]
In: Oberwolfach reports, 15 (2018) 4, pp. 2953-2954inJournal
2018
Journal Open Access
Instationary generalized Stokes equations in partially periodic domains
In: Journal of mathematical fluid mechanics, 20 (2018) 2, pp. 289-327inJournal
2018
Repository Open Access
Metastability of the Cahn-Hilliard equation in one space dimension
In: Journal of differential equations, 265 (2018) 4, pp. 1528-1575Book
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)
inJournal
2017
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Moment bounds on the corrector of stochastic homogenization of non-symmetric elliptic finite difference equations
In: Communications in partial differential equations, 42 (2017) 2, pp. 179-234inJournal
2017
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Dimension reduction techniques for the minimization of theta functions on lattices
In: Journal of mathematical physics, 58 (2017) 7, p. 071902inJournal
2017
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Kinetic selection principle for curl-free vector fields of unit norm
In: Communications in partial differential equations, 42 (2017) 9, pp. 1375-1402inJournal
2017
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Global attractor for a Ginzburg-Landau type model of rotating Bose-Einstein condensates
In: Dynamics of partial differential equations, 14 (2017) 1, pp. 5-32Preprint
2017
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Approximating conditional distributions
inJournal
2017
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Exit laws of isotropic diffusions in random environment from large domains
In: Electronic journal of probability, 22 (2017), p. 63inJournal
2017
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On the existence of an invariant measure for isotropic diffusions in random environment
In: Probability theory and related fields, 168 (2017) 1-2, pp. 409-453inJournal
2017
Journal Open Access
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. 220-255inBook
2017
Repository Open Access
Nonlocally maximal and premaximal hyperbolic sets
In: Modern theory of dynamical systems : a tribute to Dmitry Victorovich Anosov / Anatole Katok... (eds.)Providence, Rhode Island : American Mathematical Society, 2017. - pp. 83-99
(Contemporary mathematics ; 692)
inJournal
2017
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