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Singularities and Compactness in Nonlinear PDEs

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Publications

Relaxation for Partially Coercive Integral Functionals with Linear Growth

Author(s): Filip Rindler, Giles Shaw
Published in: SIAM Journal on Mathematical Analysis, Issue 52/5, 2020, Page(s) 4806-4860, ISSN 0036-1410
DOI: 10.1137/18m1199460

Fine properties of functions of bounded deformation -- an approach via linear PDEs

Author(s): Guido De Philippis; Filip Rindler
Published in: Mathematics in Engineering, Vol 2, Iss 3, Issue 9, 2020, Page(s) 386-422, ISSN 2640-3501
DOI: 10.3934/mine.2020018/fulltext.html

Critical $\mathrm {L}^p$-differentiability of $\mathrm {BV}^\mathbb {A}$-maps and canceling operators

Author(s): Bogdan Raiţă
Published in: Transactions of the American Mathematical Society, Issue 372/10, 2019, Page(s) 7297-7326, ISSN 0002-9947
DOI: 10.1090/tran/7878

Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints

Author(s): Adolfo Arroyo-Rabasa, Guido De Philippis, Filip Rindler
Published in: Advances in Calculus of Variations, Issue 13/3, 2020, Page(s) 219-255, ISSN 1864-8258
DOI: 10.1515/acv-2017-0003

Concentration versus Oscillation Effects in Brittle Damage

Author(s): Jean‐François Babadjian, Flaviana Iurlano, Filip Rindler
Published in: Communications on Pure and Applied Mathematics, Issue Online First, 2020, ISSN 0010-3640
DOI: 10.1002/cpa.21953

An elementary approach to the dimension of measures satisfying a first-order linear PDE constraint

Author(s): Adolfo Arroyo-Rabasa
Published in: Proceedings of the American Mathematical Society, Issue 148/1, 2020, Page(s) 273-282, ISSN 0002-9939
DOI: 10.1090/proc/14732

A note on estimates for elliptic systems with L1 data

Author(s): Bogdan Raita, Daniel Spector
Published in: Comptes Rendus Mathematique, Issue 357/11-12, 2019, Page(s) 851-857, ISSN 1631-073X
DOI: 10.1016/j.crma.2019.11.007

Generalized Multiscale Young Measures

Author(s): Adolfo Arroyo-Rabasa, Johannes Diermeier
Published in: SIAM Journal on Mathematical Analysis, Issue 52/4, 2020, Page(s) 3252-3300, ISSN 0036-1410
DOI: 10.1137/19m1238848

Continuity and canceling operators of order n on $${\mathbb {R}}^n$$

Author(s): Bogdan Raiță, Anna Skorobogatova
Published in: Calculus of Variations and Partial Differential Equations, Issue 59/2, 2020, Page(s) Article no. 85, ISSN 0944-2669
DOI: 10.1007/s00526-020-01739-z

On the relaxation of integral functionals depending on the symmetrized gradient

Author(s): Kosiba, Kamil; Rindler, Filip
Published in: Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Issue Published online, 2020, ISSN 0308-2105
DOI: 10.1017/prm.2020.22

Dimensional estimates and rectifiability for measures satisfying linear PDE constraints

Author(s): Adolfo Arroyo-Rabasa, Guido De Philippis, Jonas Hirsch, Filip Rindler
Published in: Geometric and Functional Analysis, Issue 29/3, 2019, Page(s) 639-658, ISSN 1016-443X
DOI: 10.1007/s00039-019-00497-1

Liftings, Young Measures, and Lower Semicontinuity

Author(s): Filip Rindler, Giles Shaw
Published in: Archive for Rational Mechanics and Analysis, Issue 232/3, 2019, Page(s) 1227-1328, ISSN 0003-9527
DOI: 10.1007/s00205-018-01343-8

On the two-state problem for general differential operators

Author(s): Guido De Philippis, Luca Palmieri, Filip Rindler
Published in: Nonlinear Analysis, Issue 177, 2018, Page(s) 387-396, ISSN 0362-546X
DOI: 10.1016/j.na.2018.03.015

Critical $\mathrm {L}^p$-differentiability of $\mathrm {BV}^\mathbb {A}$-maps and canceling operators

Author(s): Bogdan Raiţă
Published in: Transactions of the American Mathematical Society, 2019, Page(s) 1, ISSN 0002-9947
DOI: 10.1090/tran/7878

Embeddings for A -weakly differentiable functions on domains

Author(s): Franz Gmeineder, Bogdan Raiţă
Published in: Journal of Functional Analysis, Issue 277/12, 2019, Page(s) 108278, ISSN 0022-1236
DOI: 10.1016/j.jfa.2019.108278

An elementary approach to the dimension of measures satisfying a first-order linear PDE constraint

Author(s): Adolfo Arroyo-Rabasa
Published in: Proceedings of the American Mathematical Society, 2019, Page(s) 1, ISSN 0002-9939
DOI: 10.1090/proc/14732

ON THE STRUCTURE OF MEASURES CONSTRAINED BY LINEAR PDES

Author(s): GUIDO DE PHILIPPIS, FILIP RINDLER
Published in: Proceedings of the International Congress of Mathematicians (ICM 2018), 2019, Page(s) 2215-2239
DOI: 10.1142/9789813272880_0136