Singularities and Compactness in Nonlinear PDEs

Project Information

SINGULARITY

Grant agreement ID: 757254

DOI 10.3030/757254

Project closed

EC signature date 9 November 2017

Start date 1 April 2018

End date 31 March 2024

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost € 1 483 943,00

EU contribution € 1 483 943,00

Coordinated by

UNIVERSITY OF WARWICK
United Kingdom

Publications

Peer reviewed articles (37)

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
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/18m1199460

Energetic solutions to rate-independent large-strain elasto-plastic evolutions driven by discrete dislocation flow

Author(s): Rindler, Filip
Published in: Journal of the European Mathematical Society, Issue Online First, 2024, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1424

Weak and parabolic solutions of advection–diffusion equations with rough velocity field

Author(s): Paolo Bonicatto; Gennaro Ciampa; Gianluca Crippa
Published in: Journal of Evolution Equations, Issue 24, 2023, Page(s) Article No 1, ISSN 1424-3199
Publisher: Birkhauser Verlag
DOI: 10.1007/s00028-023-00919-6

Rectifiability of the jump set of locally integrable functions

Author(s): Giacomo Del Nin
Published in: Ann. Sc. Norm. Super. Pisa Cl. Sci., Issue 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, Issue 9, 2020, Page(s) 386-422, ISSN 2640-3501
Publisher: AIMS Publishing
DOI: 10.3934/mine.2020018/fulltext.html

Characterization of Generalized Young Measures Generated by $${\mathcal {A}}$$ A -free Measures

Author(s): Adolfo Arroyo-Rabasa
Published in: Archive for Rational Mechanics and Analysis, Issue 242, 2021, Page(s) 235–325, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-021-01683-y

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
Publisher: American Mathematical Society
DOI: 10.1090/tran/7878

Quasiconvexity, Null Lagrangians, and Hardy Space Integrability Under Constant Rank Constraints

Author(s): André Guerra; Bogdan Raiță
Published in: Archive for Rational Mechanics and Analysis, Issue 245, 2022, Page(s) 279-329, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-022-01775-3

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
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, Issue 00221236, 2022, Page(s) 109378, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2021.109378

Two-speed solutions to non-convex rate-independent systems

Author(s): Rindler, Filip; Schwarzacher, Sebastian; Velazquez, Juan J. L.
Published in: Archive for Rational Mechanics and Analysis, Issue 17, 2021, Page(s) 1667–1731, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.48550/arxiv.1907.05035

On limiting trace inequalities for vectorial differential operators

Author(s): Gmeineder, Franz; Raita, Bogdan; Van Schaftingen, Jean
Published in: Indiana University Mathematics Journal, Issue Vol. 70, no.5, 2021, Page(s) 2133-2176, ISSN 0022-2518
Publisher: Indiana University Press
DOI: 10.1512/iumj.2021.70.8682

Oscillation and Concentration in Sequences of PDE Constrained Measures

Author(s): Kristensen, Jan; Raiță, Bogdan
Published in: Archive for Rational Mechanics and Analysis, Issue 246, 2022, Page(s) 823-875, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-022-01828-7

Representation of the total variation as a \gamma-limit of BMO-type seminorms

Author(s): Arroyo-Rabasa, Adolfo; Bonicatto, Paolo; Del Nin, Giacomo
Published in: Indiana University Mathematics Journal, Issue 73, 2024, Page(s) 341–365, ISSN 0022-2518
Publisher: Indiana University Press
DOI: 10.1512/iumj.2024.73.9789

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
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., Issue 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, Issue 148/1, 2020, Page(s) 273-282, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/14732

Space-time integral currents of bounded variation

Author(s): Filip Rindler
Published in: Calculus of Variations and Partial Differential Equations, Issue 62, 2023, Page(s) Article No 54, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-022-02332-2

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
Publisher: Elsevier Masson
DOI: 10.1016/j.crma.2019.11.007

Shape optimization of light structures and the vanishing mass conjecture

Author(s): Babadjian, Jean-François; Iurlano, Flaviana; Rindler, Filip
Published in: Duke Mathematical Journal, Issue 172(1), 2023, Page(s) 43-103, ISSN 0012-7094
Publisher: Duke University Press
DOI: 10.1215/00127094-2022-0031

A Bourgain–Brezis–Mironescu representation for functions with bounded deformation

Author(s): Adolfo Arroyo-Rabasa; Paolo Bonicatto
Published in: Calculus of Variations and Partial Differential Equations, Issue 62, 2023, Page(s) Article No 33, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-022-02350-0

Existence and uniqueness for the transport of currents by Lipschitz vector fields

Author(s): Bonicatto, Paolo; Del Nin, Giacomo; Rindler, Filip
Published in: Journal of Functional Analysis, Issue 286, Issue 7, 2024, Page(s) 110315, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2024.110315

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

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

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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 177, 2018, Page(s) 387-396, ISSN 0362-546X
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.na.2018.03.015

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
Publisher: Academic Press
DOI: 10.1016/j.jfa.2019.108278

On the structure of divergence-free measures in R2

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

Degenerate Elastic Networks

Author(s): Del Nin, Giacomo; Pluda, Alessandra; Pozzetta, Marco
Published in: Journal of Geometric Analysis, Issue 31, 2021, Page(s) 6128–6170, ISSN 1050-6926
Publisher: American Mathematical Society
DOI: 10.1007/s12220-020-00521-z

Debye screening for the stationary Vlasov-Poisson equation in interaction with a point charge

Author(s): Arroyo-Rabasa, Adolfo; Winter, Raphael
Published in: Communications in Partial Differential Equations, Issue Online, 2021, Page(s) 1569-1584, ISSN 0360-5302
Publisher: Marcel Dekker Inc.
DOI: 10.1080/03605302.2021.1892754

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, Issue 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, Issue 02182025, 2022, Page(s) 851-910, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.48550/arxiv.2109.08749

Conference proceedings (2)

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