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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, 52/5, 2020, Page(s) 4806-4860, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/18m1199460

Rectifiability of the jump set of locally integrable functions

Author(s): Giacomo Del Nin
Published in: Ann. Sc. Norm. Super. Pisa Cl. Sci., 0391173X, 2021, Page(s) 1233–1240, ISSN 0391-173X
Publisher: Stampacchia Guido
DOI: 10.2422/2036-2145.202002_006

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, 9, 2020, Page(s) 386-422, ISSN 2640-3501
Publisher: AIMS Publishing
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, 372/10, 2019, Page(s) 7297-7326, ISSN 0002-9947
Publisher: American Mathematical Society
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, 13/3, 2020, Page(s) 219-255, ISSN 1864-8258
Publisher: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/acv-2017-0003

Decomposition of integral metric currents

Author(s): Paolo Bonicatto; Giacomo Del Nin; Enrico Pasqualetto
Published in: Journal of Functional Analysis, 00221236, 2022, Page(s) 109378, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2021.109378

Concentration versus Oscillation Effects in Brittle Damage

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

Geometric criteria for C1,α$C^{1,\alpha }$‐rectifiability

Author(s): Giacomo Del Nin; Kennedy Obinna Idu
Published in: J. Lond. Math. Soc., 00246107, 2022, Page(s) 445–468, ISSN 0024-6107
Publisher: Oxford University Press
DOI: 10.1112/jlms.12520

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, 148/1, 2020, Page(s) 273-282, ISSN 0002-9939
Publisher: American Mathematical Society
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, 357/11-12, 2019, Page(s) 851-857, ISSN 1631-073X
Publisher: Elsevier Masson
DOI: 10.1016/j.crma.2019.11.007

On the advection-diffusion equation with rough coefficients: Weak solutions and vanishing viscosity

Author(s): Paolo Bonicatto; Gennaro Ciampa; Gianluca Crippa
Published in: Journal de Mathématiques Pures et Appliquées, 00217824, 2022, Page(s) 204-224, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.1016/j.matpur.2022.09.005

Generalized Multiscale Young Measures

Author(s): Adolfo Arroyo-Rabasa, Johannes Diermeier
Published in: SIAM Journal on Mathematical Analysis, 52/4, 2020, Page(s) 3252-3300, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
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, 59/2, 2020, Page(s) Article no. 85, ISSN 0944-2669
Publisher: Springer Verlag
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, Published online, 2020, ISSN 0308-2105
Publisher: The RSE Scotland Foundation
DOI: 10.1017/prm.2020.22

Endpoint Fourier restriction and unrectifiability

Author(s): Giacomo Del Nin; Andrea Merlo
Published in: Proceedings of the American Mathematical Society, 00029939, 2022, Page(s) 2137–2144, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.48550/arxiv.2104.07482

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, 29/3, 2019, Page(s) 639-658, ISSN 1016-443X
Publisher: Birkhauser Verlag
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, 232/3, 2019, Page(s) 1227-1328, ISSN 0003-9527
Publisher: Springer Verlag
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, 177, 2018, Page(s) 387-396, ISSN 0362-546X
Publisher: Pergamon Press Ltd.
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
Publisher: American Mathematical Society
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, 277/12, 2019, Page(s) 108278, ISSN 0022-1236
Publisher: Academic Press
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
Publisher: American Mathematical Society
DOI: 10.1090/proc/14732

On the structure of divergence-free measures in R2

Author(s): Paolo Bonicatto; Nikolay A. Gusev
Published in: Advances in Calculus of Variations, 18648258, 2021, Page(s) 879-911, ISSN 1864-8258
Publisher: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/acv-2020-0066

Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings

Author(s): Del Nin, Giacomo; Petrache, Mircea
Published in: Calculus of Variations and Partial Differential Equations, 09442669, 2022, Page(s) Article number: 226, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.48550/arxiv.2101.11977

Elasto-plastic evolution of single crystals driven by dislocation flow

Author(s): Thomas Hudson; Filip Rindler
Published in: Mathematical Models and Methods in Applied Sciences, 02182025, 2022, Page(s) 851-910, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.48550/arxiv.2109.08749

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, ISBN 978-981-327-288-0
Publisher: WORLD SCIENTIFIC
DOI: 10.1142/9789813272880_0136

Model inference for Ordinary Differential Equations by parametric polynomial kernel regression

Author(s): David Green; Filip Rindler
Published in: 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, 2020, Page(s) 263-285
Publisher: www.eccomasproceedia.org
DOI: 10.7712/120219.6340.18533