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

Publications

Peer reviewed articles (12)

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

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

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

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

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

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

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

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

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