Variational approach to the regularity of the free boundaries

Project Information

VAREG

Grant agreement ID: 853404

DOI

10.3030/853404

EC signature date 27 February 2020

Start date 1 June 2020

End date 30 November 2025

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 330 325,00

EU contribution

€ 1 330 325,00

Coordinated by

UNIVERSITA DI PISA
Italy

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

Book chapters (1)

Isoperimetric Sets in Nonnegative Scalar Curvature and Their Role Through Various Concepts of Mass

Author(s): Luca Benatti, Mattia Fogagnolo
Published in: Springer INdAM Series, Anisotropic Isoperimetric Problems and Related Topics, 2024, Page(s) 169-199
Publisher: Springer Nature Singapore
DOI: 10.1007/978-981-97-6984-1_8

Peer reviewed articles (33)

Regularity of shape optimizers for some spectral fractional problems

Author(s): Giorgio Tortone
Published in: Journal of Functional Analysis, Issue 1, 2021, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2021.109271

Regularity of the optimal sets for the second Dirichlet eigenvalue

Author(s): Mazzoleni, Dario; Trey, Baptiste; Velichkov, Bozhidar
Published in: Annales de l'Institut Henri Poincaré C, Issue 39, 2022, Page(s) 529-573, ISSN 0294-1449
Publisher: Elsevier BV
DOI: 10.48550/arxiv.2010.00441

A Short Proof of Allard’s and Brakke’s Regularity Theorems

Author(s): Guido De Philippis, Carlo Gasparetto, Felix Schulze
Published in: International Mathematics Research Notices, Issue 2024, 2024, Page(s) 7594-7613, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnad281

Numerical computation of the cut locus via a variational approximation of the distance function

Author(s): François Générau, Edouard Oudet, Bozhidar Velichkov
Published in: ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN), 2022, ISSN 2822-7840
Publisher: EDP Sciences

Epsilon-regularity for the solutions of a free boundary system

Author(s): Francesco Paolo Maiale, Giorgio Tortone, Bozhidar Velichkov
Published in: Revista Matemática Iberoamericana, 2023, ISSN 0213-2230
Publisher: Universidad Autonoma de Madrid
DOI: 10.4171/rmi/1430

Regularity of the Optimal Sets for a Class of Integral Shape Functionals

Author(s): Giuseppe Buttazzo, Francesco Paolo Maiale, Dario Mazzoleni, Giorgio Tortone, Bozhidar Velichkov
Published in: Archive for Rational Mechanics and Analysis, Issue 248, 2024, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-024-01984-y

On the Nodal Set of Solutions to Some Sublinear Equations Without Homogeneity

Author(s): Nicola Soave, Giorgio Tortone
Published in: Archive for Rational Mechanics and Analysis, Issue 248, 2024, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-024-01970-4

Liouville theorems and optimal regularity in elliptic equations

Author(s): Giorgio Tortone
Published in: Proceedings of the London Mathematical Society, Issue 128, 2024, ISSN 0024-6115
Publisher: Oxford University Press
DOI: 10.1112/plms.12587

Free boundary cluster with Robin condition on the transmission interface

Author(s): Serena Guarino Lo Bianco, Domenico Angelo La Manna, Bozhidar Velichkov
Published in: Calculus of Variations and Partial Differential Equations, Issue 64, 2025, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-024-02864-9

Regularity for one-phase Bernoulli problems with discontinuous weights and applications

Author(s): Lorenzo Ferreri, Bozhidar Velichkov
Published in: Transactions of the American Mathematical Society, Issue 377, 2024, Page(s) 7847-7876, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/9248

On the logarithmic epiperimetric inequality for the obstacle problem

Author(s): Luca Spolaor; Bozhidar Velichkov
Published in: Mathematics in Engineering, 2021, ISSN 2640-3501
Publisher: AIMS Press
DOI: 10.3934/mine.2021004

Sharp Behavior of Dirichlet–Laplacian Eigenvalues for a Class of Singularly Perturbed Problems

Author(s): Laura Abatangelo, Roberto Ognibene
Published in: SIAM Journal on Mathematical Analysis, Issue 56, 2024, Page(s) 474-500, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/23m1564444

A two-phase problem with Robin conditions on the free boundary

Author(s): Serena Guarino Lo Bianco; Domenico Angelo La Manna; Bozhidar Velichkov
Published in: Journal de l'Ecole polytechnique - Mathematiques, 2021, ISSN 2429-7100
Publisher: Ecole polytechnique
DOI: 10.5802/jep.139

The regularity problem in domains with lower dimensional boundaries

Author(s): Zanbing Dai; Joseph Feneuil; Svitlana Mayboroda
Published in: Journal of Functional Analysis, Issue 284, 2023, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2023.109903

Green function estimates on complements of low-dimensional uniformly rectifiable sets

Author(s): Guy David, Joseph Feneuil, Svitlana Mayboroda
Published in: Mathematische Annalen, Issue 385, 2023, Page(s) 1797-1821, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-022-02379-8

Effects of surface tension and elasticity on critical points of the Kirchhoff–Plateau problem

Author(s): Giulia Bevilacqua, Chiara Lonati
Published in: Bollettino dell'Unione Matematica Italiana, Issue 17, 2024, Page(s) 221-240, ISSN 1972-6724
Publisher: Unione Matematica Italiana
DOI: 10.1007/s40574-023-00392-6

A vectorial problem with thin free boundary

Author(s): Daniela De Silva, Giorgio Tortone
Published in: Calculus of Variations and Partial Differential Equations, Issue 62, 2023, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-023-02561-z

Regularity of the optimal sets for the second Dirichlet eigenvalue

Author(s): Mazzoleni, Dario; Trey, Baptiste; Velichkov, Bozhidar
Published in: Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 2022, ISSN 0294-1449
Publisher: Elsevier BV
DOI: 10.4171/aihpc/14

Green functions and smooth distances

Author(s): Joseph Feneuil, Linhan Li, Svitlana Mayboroda
Published in: Mathematische Annalen, Issue 389, 2024, Page(s) 2637-2727, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-023-02715-6

Cut locus on compact manifolds and uniform semiconcavity estimates for a variational inequality

Author(s): François Générau; Édouard Oudet; Bozhidar Velichkov
Published in: Archive for Rational Mechanics and Analysis volume, Issue 246, 2022, Page(s) 561-602, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-022-01821-0

Elastic membranes spanning deformable curves

Author(s): Francesco Ballarin, Giulia Bevilacqua, Luca Lussardi, Alfredo Marzocchi
Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Issue 104, 2024, ISSN 0044-2267
Publisher: John Wiley & Sons Ltd.
DOI: 10.1002/zamm.202300890

On the isoperimetric Riemannian Penrose inequality

Author(s): Luca Benatti, Mattia Fogagnolo, Lorenzo Mazzieri
Published in: Communications on Pure and Applied Mathematics, 2024, ISSN 0010-3640
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/cpa.22239

Regularity of the free boundary for the two-phase Bernoulli problem

Author(s): Guido De Philippis, Luca Spolaor, Bozhidar Velichkov
Published in: Inventiones Mathematicae, 2021, ISSN 1432-1297
Publisher: Springer
DOI: 10.1007/s00222-021-01031-7

Carleson perturbations for the regularity problem

Author(s): Zanbing Dai, Joseph Feneuil, Svitlana Mayboroda
Published in: Revista Matemática Iberoamericana, Issue 39, 2024, Page(s) 2119-2170, ISSN 0213-2230
Publisher: Universidad Autonoma de Madrid
DOI: 10.4171/rmi/1401

Shape optimization problems in control form

Author(s): Giuseppe Buttazzo, Francesco Paolo Maiale, Bozhidar Velichkov
Published in: RENDICONTI LINCEI - MATEMATICA E APPLICAZIONI, 2021, ISSN 1120-6330
Publisher: Accademia Nazionale dei Lincei
DOI: 10.4171/rlm/942

Higher Order Boundary Harnack Principle via Degenerate Equations

Author(s): Susanna Terracini, Giorgio Tortone, Stefano Vita
Published in: Archive for Rational Mechanics and Analysis, Issue 248, 2024, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-024-01973-1

(Quasi-)conformal methods in two-dimensional free boundary problems

Author(s): Guido De Philippis, Luca Spolaor, Bozhidar Velichkov
Published in: Journal of the European Mathematical Society, 2024, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1435

Nonlinear Isocapacitary Concepts of Mass in 3-Manifolds with Nonnegative Scalar Curvature

Author(s): null null, Luca Benatti, null null, null null, Mattia Fogagnolo, null null, Lorenzo Mazzieri, null null
Published in: Symmetry, Integrability and Geometry: Methods and Applications, 2023, ISSN 1815-0659
Publisher: Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine
DOI: 10.3842/sigma.2023.091

The boundary Harnack principle on optimal domains

Author(s): Francesco Paolo Maiale, Giorgio Tortone, Bozhidar Velichkov
Published in: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2022, ISSN 0391-173X
Publisher: Stampacchia Guido
DOI: 10.2422/2036-2145.202112_003

Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem

Author(s): Maria Colombo; Luca Spolaor; Bozhidar Velichkov
Published in: Interfaces and Free Boundaries, Issue 2, 2021, ISSN 1463-9963
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/ifb/452

On the spectrum of sets made of cores and tubes

Author(s): Francesca Bianchi, Lorenzo Brasco, Roberto Ognibene
Published in: Journal of Convex Analysis, 2024, ISSN 0944-6532
Publisher: Heldermann Verlag

The symmetric (log-)epiperimetric inequality and a decay-growth estimate

Author(s): Nick Edelen, Luca Spolaor, Bozhidar Velichkov
Published in: Calculus of Variations and Partial Differential Equations, Issue 63, 2024, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-023-02610-7

Global Solutions for Two-Phase Complex Fluids with Quadratic Anchoring in Soft Matter Physics

Author(s): Giulia Bevilacqua, Andrea Giorgini
Published in: SIAM Journal on Mathematical Analysis, Issue 56, 2024, Page(s) 6057-6120, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/23m1608902

Monographic books (1)

Regularity of the One-phase Free Boundaries

Author(s): Bozhidar Velichkov
Published in: Lecture Notes of the Unione Matematica Italiana, 2023, ISBN 978-3-031-13237-7
Publisher: Springer International Publishing
DOI: 10.1007/978-3-031-13238-4