Regularity and singularities in elliptic PDE's: beyond monotonicity formulas

Project Information

EllipticPDE

Grant agreement ID: 801867

DOI 10.3030/801867

Project closed

EC signature date 22 August 2018

Start date 1 January 2019

End date 30 September 2024

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost € 1 335 250,00

EU contribution € 1 335 250,00

Coordinated by

UNIVERSITAT DE BARCELONA
Spain

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 (26)

Carleman estimates with sharp weights and boundary observability for wave operators with critically singular potentials

Author(s): A. Enciso, A. Shao, B. Vergara
Published in: J. Eur. Math. Soc., 2020, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1105

Global Schauder theory for minimizers of the Hs(Ω) energy

Author(s): Mouhamed Moustapha Fall, Xavier Ros-Oton
Published in: Journal of Functional Analysis, 2022, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2022.109523

Non-symmetric stable operators: regularity theory and integration by parts

Author(s): Serena Dipierro, Xavier Ros-Oton, Joaquim Serra, Enrico Valdinoci
Published in: Advances in Mathematics, 2022, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2022.108321

New boundary Harnack inequalities with right hand side

Author(s): Xavier Ros-Oton, Damià Torres-Latorre
Published in: Journal of Differential Equations, Issue 288, 2021, Page(s) 204-249, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2021.04.012

Generic regularity of free boundaries for the obstacle problem

Author(s): Alessio Figalli, Xavier Ros-Oton, Joaquim Serra
Published in: Publications mathématiques de l'IHÉS, 2020, ISSN 0073-8301
Publisher: Springer Verlag
DOI: 10.1007/s10240-020-00119-9

C^{2,\alpha} regularity of free boundaries in parabolic non-local obstacle problems

Author(s): Teo Kukuljan
Published in: Calculus of Variations and Partial Differential Equations, 2023, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-022-02372-8

The concentration-compactness principle for the nonlocal anisotropic p-Laplacian of mixed order

Author(s): Jamil Chaker, Minhyun Kim, Marvin Weidner
Published in: Nonlinear Analysis, 2023, ISSN 0362-546X
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.na.2023.113254

Optimal regularity and fine asymptotics for the porous medium equation in bounded domains

Author(s): Tianling Jin, Xavier Ros-Oton, Jingang Xiong
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal), 2024, ISSN 0075-4102
Publisher: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/crelle-2024-0014

Optimal regularity for supercritical parabolic obstacle problems

Author(s): Xavier Ros‐Oton, Clara Torres‐Latorre
Published in: Communications on Pure and Applied Mathematics, Issue 77, 2024, Page(s) 1724-1765, ISSN 0010-3640
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/cpa.22166

A minimization procedure to the existence of segregated solutions to parabolic reaction-diffusion systems

Author(s): Audrito, Alessandro; Serra, Enrico; Tilli, Paolo
Published in: Comm. PDE, 2021, ISSN 0360-5302
Publisher: Marcel Dekker Inc.
DOI: 10.1080/03605302.2021.1931884

Sharp quantitative stability for isoperimetric inequalities with homogeneous weights

Author(s): Cinti, Eleonora; Glaudo, Federico; Pratelli, Aldo; Ros-Oton, Xavier; Serra, Joaquim
Published in: Trans. AMS, 2022, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/8525

Stable solutions to semilinear elliptic equations are smooth up to dimension $9$

Author(s): Xavier Cabré, Alessio Figalli, Xavier Ros-Oton, Joaquim Serra
Published in: Acta Mathematica, Issue 224/2, 2020, Page(s) 187-252, ISSN 0001-5962
Publisher: Royal Swedish Academy of Sciences
DOI: 10.4310/acta.2020.v224.n2.a1

Upper heat kernel estimates for nonlocal operators via Aronson’s method

Author(s): Moritz Kassmann, Marvin Weidner
Published in: Calculus of Variations and Partial Differential Equations, Issue 62, 2023, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-022-02398-y

Obstacle problems for integro-differential operators: Higher regularity of free boundaries

Author(s): Nicola Abatangelo, Xavier Ros-Oton
Published in: Advances in Mathematics, Issue 360, 2020, Page(s) 106931, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2019.106931

Stable cones in the thin one-phase problem

Author(s): Xavier Fernández-Real, Xavier Ros-Oton
Published in: American Journal of Mathematics, Issue 146, 2024, Page(s) 631-685, ISSN 1080-6377
Publisher: Johns Hopkins University Press
DOI: 10.1353/ajm.2024.a928321

Free Boundary Regularity for Almost Every Solution to the Signorini Problem

Author(s): Fernández-Real, Xavier; Ros-Oton, Xavier
Published in: Arch. Rat. Mech. Anal., Issue 240, 2021, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-021-01617-8

The singular set in the Stefan problem

Author(s): Alessio Figalli, Xavier Ros-Oton, Joaquim Serra
Published in: Journal of the AMS, 2024, ISSN 0894-0347
Publisher: American Mathematical Society
DOI: 10.1090/jams/1026

Runge approximation and stability improvement for a partial data Calderón problem for the acoustic Helmholtz equation

Author(s): A. Ruland, M. A. Garcia-Ferrero, W. Zaton
Published in: Inverse problems and imaging, 2022, ISSN 1930-8337
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/ipi.2021049

The Neumann problem for the fractional Laplacian: regularity up to the boundary

Author(s): Audrito, Alessandro; Felipe-Navarro, Juan-Carlos; Ros-Oton, Xavier
Published in: Ann. Sc. Norm. Super. Pisa Cl. Sci., 2022, ISSN 0391-173X
Publisher: Stampacchia Guido
DOI: 10.2422/2036-2145.202105_096

The Dirichlet problem for nonlocal elliptic operators with $C^{0,\alpha }$ exterior data

Author(s): Alessandro Audrito, Xavier Ros-Oton
Published in: Proceedings of the American Mathematical Society, Issue 148/10, 2020, Page(s) 4455-4470, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/15121

Generic regularity of free boundaries for the thin obstacle problem

Author(s): Xavier Fernández-Real, Clara Torres-Latorre
Published in: Advances in Mathematics, Issue 433, 2023, Page(s) 109323, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2023.109323

The fractional obstacle problem with drift: Higher regularity of free boundaries

Author(s): Teo Kukuljan
Published in: Journal of Functional Analysis, Issue 281/8, 2021, Page(s) 109114, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2021.109114

Regularity for nonlocal problems with non-standard growth

Author(s): Jamil Chaker, Minhyun Kim, Marvin Weidner
Published in: Calculus of Variations and Partial Differential Equations, Issue 61, 2023, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-022-02364-8

Higher order parabolic boundary Harnack inequality in $C^1$ and $C^{k,\alpha}$ domains

Author(s): Kukuljan, Teo
Published in: Disc. Cont. Dyn. Syst., 2022, ISSN 1078-0947
Publisher: Dept. of Mathematics, Southwest Missouri State University
DOI: 10.3934/dcds.2021207

Regularity theory for fully nonlinear parabolic obstacle problems

Author(s): Alessandro Audrito, Teo Kukuljan
Published in: Journal of Functional Analysis, Issue 285, 2023, Page(s) 110116, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2023.110116

Optimal regularity for the fully nonlinear thin obstacle problem

Author(s): Maria Colombo, Xavier Fernández-Real, Xavier Ros-Oton
Published in: Journal of the European Mathematical Society, 2024, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1445

Monographic books (1)

Regularity Theory for Elliptic PDE

Author(s): Xavier Fernández-Real, Xavier Ros-Oton
Published in: Zurich Lectures in Advanced Mathematics, 2022, ISBN 978-3-98547-028-0
Publisher: EMS Press
DOI: 10.4171/zlam/28