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

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

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 105, 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