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Stable interfaces: phase transitions, minimal surfaces, and free boundaries


The singular set in the Stefan problem

Author(s): Alessio Figalli, Xavier Ros-Oton, Joaquim Serra
Published in: Journal of the American Mathematical Society, 2023, ISSN 0894-0347
Publisher: American Mathematical Society

Interface regularity for semilinear one-phase problems

Author(s): Audrito, Alessandro; Serra, Joaquim
Published in: Advances in Mathematics, 403, 2022, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2022.108380

Stable solutions to the fractional Allen-Cahn equation inthe nonlocal perimeter regime

Author(s): Xabier Cabré, Eleonora Cinti, Joaquim Serra
Published in: American Journal of Mathematics, 2023, ISSN 0002-9327
Publisher: The Johns Hopkins University Press

Free boundary partial regularity in the thin obstacle problem,

Author(s): Federico Franceschini, Joaquim Serra,
Published in: Communications on Pure and Applied Mathematics, 2023, ISSN 0010-3640
Publisher: John Wiley & Sons Inc.

Yau's conjecture for nonlocal minimal surfaces

Author(s): Caselli, Michele; Florit-Simon, Enric; Serra, Joaquim
Published in: arXiv, Issue 3, 2023, ISSN 2331-8422
DOI: 10.48550/arxiv.2306.07100

Fractional Sobolev spaces on Riemannian manifolds

Author(s): Michele Caselli, Enric Florit-Simon, Joaquim Serra
Published in: arXiv, 2024, ISSN 2331-8422

Partial regularity for $BV^\mathcal{B}$ minimizers

Author(s): Franceschini, Federico
Published in: arXIv, Issue 4, 2023, ISSN 2331-8422
DOI: 10.48550/arxiv.2310.20002

The Structure of the Regular Part of the Free Boundary Close to Singularities in the Obstacle Problem

Author(s): Simon Eberle; Henrik Shahgholian; Georg S. Weiss
Published in: Crossref, Issue 2, 2021, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.2139/ssrn.4296060

Regularity theory for nonlocal obstacle problems with critical and subcritical scaling

Author(s): Figalli, Alessio; Ros-Oton, Xavier; Serra, Joaquim
Published in: arXiv, Issue 8, 2023, ISSN 2331-8422
DOI: 10.48550/arxiv.2306.16008

Elliptic regularization of some semilinear parabolic free boundary problems

Author(s): Alessandro Audrito; Tomás Sanz-Perela
Published in: arXiv, Issue 5, 2023, ISSN 2331-8422
DOI: 10.4171/ifb/511

Nonlocal approximation of minimal surfaces: optimal estimates from stability

Author(s): Chan, Hardy; Dipierro, Serena; Serra, Joaquim; Valdinoci, Enrico
Published in: arXiv, Issue 7, 2023, ISSN 2331-8422
DOI: 10.48550/arxiv.2308.06328

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