Rigidity and Flexibility in PDEs

Head:
Angkana Rüland (Email)

Phone:
+49 (0) 341 - 9959 - 953

Fax:
+49 (0) 341 - 9959 - 658

Address:
Inselstr. 22
04103 Leipzig

Institute publications of the group

Journal Articles

Cekić, Mihajilo ; Lin, Yi-Hsuan and Rüland, Angkana: The Calderón problem for the fractional Schrödinger equation with drift
In: Calculus of variations and partial differential equations, 59 (2020) 3, 91
Bibtex DOI: 10.1007/s00526-020-01740-6 ARXIV: https://arxiv.org/abs/1810.04211
Journal Open Access

Cesana, Pierluigi ; Della Porta, Francesco ; Rüland, Angkana ; Zillinger, Christian and Zwicknagl, Barbara: Exact constructions in the (non-linear) planar theory of elasticity : from elastic crystals to nematic elastomers
In: Archive for rational mechanics and analysis, 237 (2020) 1, p. 383-445
Bibtex DOI: 10.1007/s00205-020-01511-9 ARXIV: https://arxiv.org/abs/1904.08820
Repository Open Access

Della Porta, Francesco and Rüland, Angkana: Convex integration solutions for the geometrically non-linear two-well problem with higher Sobolev regularity
In: Mathematical models and methods in applied sciences, 30 (2020) 3, p. 611-651
Bibtex DOI: 10.1142/S0218202520500153 ARXIV: https://arxiv.org/abs/1905.12521
Repository Open Access

García-Ferrero, María Angeles and Rüland, Angkana: On two methods for quantitative unique continuation results for some nonlocal operators
In: Communications in partial differential equations, Vol. not yet known, pp. not yet known
Bibtex DOI: 10.1080/03605302.2020.1776323 ARXIV: https://arxiv.org/abs/2003.06402
Repository Open Access

Ghosh, Tuhin ; Rüland, Angkana ; Salo, Mikko and Uhlmann, Gunther: Uniqueness and reconstruction for the fractional Calderón problem with a single measurement
In: Journal of functional analysis, 279 (2020) 1, 108505
Bibtex DOI: 10.1016/j.jfa.2020.108505 ARXIV: https://arxiv.org/abs/1801.04449
Repository Open Access

Lai, Ru-Yu ; Lin, Yi-Hsuan and Rüland, Angkana: The Calderón problem for a space-time fractional parabolic equation
In: SIAM journal on mathematical analysis, 52 (2020) 3, p. 2655-2688
Bibtex DOI: 10.1137/19M1270288 ARXIV: https://arxiv.org/abs/1905.08719
Repository Open Access

Rüland, Angkana and Salo, Mikko: Quantitative approximation properties for the fractional heat equation
In: Mathematical control and related fields, 10 (2020) 1, p. 1-26
Bibtex DOI: 10.3934/mcrf.2019027 ARXIV: https://arxiv.org/abs/1708.06300
Repository Open Access

Rüland, Angkana and Salo, Mikko: The fractional Calderón problem : low regularity and stability
In: Nonlinear analysis / A, 193 (2020), 111529
Bibtex DOI: 10.1016/j.na.2019.05.010 ARXIV: https://arxiv.org/abs/1708.06294
Repository Open Access

Rüland, Angkana and Sincich, Eva: On Runge approximation and Lipschitz stability for a finite-dimensional Schrödinger inverse problem
In: Applicable analysis : an international journal, Vol. not yet known, pp. not yet known
Bibtex DOI: 10.1080/00036811.2020.1738403 ARXIV: https://arxiv.org/abs/2002.09319
Repository Open Access

Rüland, Angkana ; Zillinger, Christian and Zwicknagl, Barbara: Higher Sobolev regularity of convex integration solutions in elasticity : the planar geometrically linearized hexagonal-to-rhombic phase transformation
In: Journal of elasticity, 138 (2020) 1, p. 1-76
Bibtex DOI: 10.1007/s10659-018-09719-3 ARXIV: https://arxiv.org/abs/1610.02529
Journal Open Access

Della Porta, Francesco: A model for the evolution of highly reversible martensitic transformations
In: Mathematical models and methods in applied sciences, 29 (2019) 3, p. 493-530
Bibtex DOI: 10.1142/S0218202519500143 ARXIV: https://arxiv.org/abs/1811.07664
Repository Open Access

Della Porta, Francesco: Analysis of a moving mask hypothesis for martensitic transformations
In: Journal of nonlinear science, 29 (2019) 5, p. 2341-2384
Bibtex DOI: 10.1007/s00332-019-09546-3 ARXIV: https://arxiv.org/abs/1811.08247
Repository Open Access

Enciso, Alberto ; García-Ferrero, María Angeles and Peralta-Salas, Daniel: Approximation theorems for parabolic equations and movement of local hot spots
In: Duke mathematical journal, 168 (2019) 5, p. 897-939
Bibtex DOI: 10.1215/00127094-2018-0058 ARXIV: https://arxiv.org/abs/1710.03782
Repository Open Access

García-Ferrero, María Angeles and Rüland, Angkana: Strong unique continuation for the higher order fractional Laplacian
In: Mathematics in engineering, 1 (2019) 4, p. 715-774
Bibtex DOI: 10.3934/mine.2019.4.715 ARXIV: https://arxiv.org/abs/1902.09851
Journal Open Access

Kitavtsev, Georgy ; Lauteri, Gianluca ; Luckhaus, Stephan and Rüland, Angkana: A compactness and structure result for a discrete multi-well problem with \(\text{SO}(n)\) symmetry in arbitrary dimension
In: Archive for rational mechanics and analysis, 232 (2019) 1, p. 531-555
Bibtex DOI: 10.1007/s00205-018-1327-0 ARXIV: https://arxiv.org/abs/1711.08271
Journal Open Access

Koch, Herbert ; Rüland, Angkana and Shi, Wenhui: Higher regularity for the fractional thin obstacle problem
In: New York journal of mathematics, 25 (2019), p. 745-838
Bibtex ARXIV: https://arxiv.org/abs/1605.06662 LINK: http://nyjm.albany.edu/j/2019/25-35.html
Journal Open Access

Rüland, Angkana: Quantitative invertibility and approximation for the truncated Hilbert and Riesz transforms
In: Revista Matemática Iberoamericana, 35 (2019) 7, p. 1997-2024
Bibtex DOI: 10.4171/RMI/1107 ARXIV: https://arxiv.org/abs/1708.04285
Repository Open Access

Rüland, Angkana and Sincich, Eva: Lipschitz stability for the finite dimensional fractional Calderón problem with finite Cauchy data
In: Inverse problems and imaging, 13 (2019) 5, p. 1023-1044
Bibtex DOI: 10.3934/ipi.2019046 ARXIV: https://arxiv.org/abs/1805.00866
Repository Open Access

Rüland, Angkana ; Taylor, Jamie M. and Zillinger, Christian: Convex integration arising in the modelling of shape-memory alloys : some remarks on rigidity, flexibility and some numerical implementations
In: Journal of nonlinear science, 29 (2019) 5, p. 2137-2184
Bibtex DOI: 10.1007/s00332-019-09540-9 ARXIV: https://arxiv.org/abs/1801.08503
Repository Open Access

Rüland, Angkana and Wang, Jenn-Nan: On the fractional Landis conjecture
In: Journal of functional analysis, 277 (2019) 9, p. 3236-3270
Bibtex DOI: 10.1016/j.jfa.2019.05.026 ARXIV: https://arxiv.org/abs/1809.04480
Repository Open Access

Ayala, Diego A. ; Doering, Charles R. and Simon, Thilo Martin: Maximum palinstrophy amplification in the two-dimensional Navier-Stokes equations
In: Journal of fluid mechanics, 837 (2018), p. 839-857
Bibtex DOI: 10.1017/jfm.2017.874 ARXIV: https://arxiv.org/abs/1704.00087
Repository Open Access

Laux, Tim Bastian and Simon, Thilo Martin: Convergence of the Allen-Cahn equation to multiphase mean curvature flow
In: Communications on pure and applied mathematics, 71 (2018) 8, p. 1597-1647
Bibtex MIS-Preprint: 37/2016 DOI: 10.1002/cpa.21747 ARXIV: http://arxiv.org/abs/1606.07318
Repository Open Access

Rüland, Angkana: Unique continuation for sublinear elliptic equations based on Carleman estimates
In: Journal of differential equations, 265 (2018) 11, p. 6009-6035
Bibtex DOI: 10.1016/j.jde.2018.07.025 ARXIV: https://arxiv.org/abs/1801.05563
Repository Open Access

Rüland, Angkana and Salo, Mikko: Exponential instability in the fractional Calderón problem
In: Inverse problems, 34 (2018) 4, 045003
Bibtex DOI: 10.1088/1361-6420/aaac5a ARXIV: https://arxiv.org/abs/1711.04799
Journal Open Access

Rüland, Angkana ; Zillinger, Christian and Zwicknagl, Barbara: Higher Sobolev regularity of convex integration solutions in elasticity : the Dirichlet problem with affine data in \(\text{int}(K^{lc})\)
In: SIAM journal on mathematical analysis, 50 (2018) 4, p. 3791-3841
Bibtex DOI: 10.1137/17M1149687 ARXIV: https://arxiv.org/abs/1709.02880
Repository Open Access

Rüland, Angkana: The cubic-to-orthorhombic phase transition : rigidity and non-rigidity properties in the linear theory of elasticity
In: Archive for rational mechanics and analysis, 221 (2016) 1, p. 23-106
Bibtex MIS-Preprint: 45/2013 DOI: 10.1007/s00205-016-0971-5
Repository Open Access

Rüland, Angkana: A rigidity result for a reduced model of a cubic-to-orthorhombic phase transition in the geometrically linear theory of elasticity
In: Journal of elasticity, 123 (2016) 2, p. 137-177
Bibtex DOI: 10.1007/s10659-015-9553-2 ARXIV: https://arxiv.org/abs/1305.6200
Repository Open Access

Kitavtsev, Georgy ; Luckhaus, Stephan and Rüland, Angkana: Surface energies arising in microscopic modeling of martensitic transformations
In: Mathematical models and methods in applied sciences, 25 (2015) 4, p. 647-683
Bibtex MIS-Preprint: 29/2014 DOI: 10.1142/S0218202515500153 ARXIV: http://arxiv.org/abs/1402.5256
Repository Open Access

Preprints

Fernández-Bertolin, Aingeru ; Roncal, Luz ; Rüland, Angkana and Stan, Diana: Discrete Carleman estimates and three balls inequalities
Repository Open Access

Della Porta, Francesco: On \(\mathscr V_{II}\) junctions : non stress-free junctions between martensitic plates
Repository Open Access

Simon, Thilo Martin: Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via H-measures
Repository Open Access

Simon, Thilo Martin: Rigidity of branching microstructures in shape memory alloys
Repository Open Access

Academic Theses

Simon, Thilo Martin: Materials science-inspired problems in the calculus of variations : rigidity of shape memory alloys and multi-phase mean curvature flow
Dissertation, Universität Leipzig, 2018
Bibtex LINK: http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa2-318464
Repository Open Access
13.08.2020, 05:46