Variational approach to the regularity of the free boundaries

Información del proyecto

VAREG

Identificador del acuerdo de subvención: 853404

DOI

10.3030/853404

Proyecto cerrado

Fecha de la firma de la CE 27 Febrero 2020

Fecha de inicio 1 Junio 2020

Fecha de finalización 30 Noviembre 2025

Financiado con arreglo a

• EXCELLENT SCIENCE - European Research Council (ERC)

Coste total

€ 1 330 325,00

Aportación de la UE

€ 1 330 325,00

Coordinado por

UNIVERSITA DI PISA
Italy

CORDIS proporciona enlaces a los documentos públicos y las publicaciones de los proyectos de los programas marco HORIZONTE.

Los enlaces a los documentos y las publicaciones de los proyectos del Séptimo Programa Marco, así como los enlaces a algunos tipos de resultados específicos, como conjuntos de datos y «software», se obtienen dinámicamente de OpenAIRE .

Publicaciones

Peer reviewed articles (50)

Classical solutions to the soap film capillarity problem for plane boundaries

Autores: Giulia Bevilacqua, Salvatore Stuvard, Bozhidar Velichkov
Publicado en: Mathematische Annalen, Edición 392, 2025, Página(s) 4607-4659, ISSN 0025-5831
Editor: Springer Verlag
DOI: 10.1007/s00208-025-03172-z

A one-sided two phase Bernoulli free boundary problem

Autores: Lorenzo Ferreri, Bozhidar Velichkov
Publicado en: Journal de Mathématiques Pures et Appliquées, Edición 195, 2025, Página(s) 103659, ISSN 0021-7824
Editor: Elsevier BV
DOI: 10.1016/j.matpur.2025.103659

Regularity of shape optimizers for some spectral fractional problems

Autores: Giorgio Tortone
Publicado en: Journal of Functional Analysis, Edición 1, 2021, ISSN 0022-1236
Editor: Academic Press
DOI: 10.1016/j.jfa.2021.109271

Regularity of the optimal sets for the second Dirichlet eigenvalue

Autores: Mazzoleni, Dario; Trey, Baptiste; Velichkov, Bozhidar
Publicado en: Annales de l'Institut Henri Poincaré C, Edición 39, 2022, Página(s) 529-573, ISSN 0294-1449
Editor: Elsevier BV
DOI: 10.48550/arxiv.2010.00441

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

Autores: Guido De Philippis, Carlo Gasparetto, Felix Schulze
Publicado en: International Mathematics Research Notices, Edición 2024, 2024, Página(s) 7594-7613, ISSN 1073-7928
Editor: Oxford University Press
DOI: 10.1093/imrn/rnad281

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

Autores: François Générau, Edouard Oudet, Bozhidar Velichkov
Publicado en: ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN), 2022, ISSN 2822-7840
Editor: EDP Sciences

Epsilon-regularity for the solutions of a free boundary system

Autores: Francesco Paolo Maiale, Giorgio Tortone, Bozhidar Velichkov
Publicado en: Revista Matemática Iberoamericana, 2023, ISSN 0213-2230
Editor: Universidad Autonoma de Madrid
DOI: 10.4171/rmi/1430

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

Autores: Giuseppe Buttazzo, Francesco Paolo Maiale, Dario Mazzoleni, Giorgio Tortone, Bozhidar Velichkov
Publicado en: Archive for Rational Mechanics and Analysis, Edición 248, 2024, ISSN 0003-9527
Editor: Springer Verlag
DOI: 10.1007/s00205-024-01984-y

A survey on the optimal partition problem

Autores: Roberto Ognibene, Bozhidar Velichkov
Publicado en: La Matematica, Edición 5, 2026, ISSN 2730-9657
Editor: Springer Science and Business Media LLC
DOI: 10.1007/s44007-025-00176-8

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

Autores: Nicola Soave, Giorgio Tortone
Publicado en: Archive for Rational Mechanics and Analysis, Edición 248, 2024, ISSN 0003-9527
Editor: Springer Verlag
DOI: 10.1007/s00205-024-01970-4

Liouville theorems and optimal regularity in elliptic equations

Autores: Giorgio Tortone
Publicado en: Proceedings of the London Mathematical Society, Edición 128, 2024, ISSN 0024-6115
Editor: Oxford University Press
DOI: 10.1112/plms.12587

Free boundary cluster with Robin condition on the transmission interface

Autores: Serena Guarino Lo Bianco, Domenico Angelo La Manna, Bozhidar Velichkov
Publicado en: Calculus of Variations and Partial Differential Equations, Edición 64, 2025, ISSN 0944-2669
Editor: Springer Verlag
DOI: 10.1007/s00526-024-02864-9

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

Autores: Lorenzo Ferreri, Bozhidar Velichkov
Publicado en: Transactions of the American Mathematical Society, Edición 377, 2024, Página(s) 7847-7876, ISSN 0002-9947
Editor: American Mathematical Society
DOI: 10.1090/tran/9248

Quantitative spectral stability for the Neumann Laplacian in domains with small holes

Autores: Veronica Felli, Lorenzo Liverani, Roberto Ognibene
Publicado en: Journal of Functional Analysis, Edición 288, 2025, Página(s) 110817, ISSN 0022-1236
Editor: Academic Press
DOI: 10.1016/j.jfa.2024.110817

On the logarithmic epiperimetric inequality for the obstacle problem

Autores: Luca Spolaor; Bozhidar Velichkov
Publicado en: Mathematics in Engineering, 2021, ISSN 2640-3501
Editor: AIMS Press
DOI: 10.3934/mine.2021004

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

Autores: Laura Abatangelo, Roberto Ognibene
Publicado en: SIAM Journal on Mathematical Analysis, Edición 56, 2024, Página(s) 474-500, ISSN 0036-1410
Editor: Society for Industrial and Applied Mathematics
DOI: 10.1137/23m1564444

Eigenvalues of the Laplacian with moving mixed boundary conditions: The case of disappearing Neumann region

Autores: Veronica Felli, Benedetta Noris, Roberto Ognibene
Publicado en: Journal of Differential Equations, Edición 320, 2025, Página(s) 247-315, ISSN 0022-0396
Editor: Academic Press
DOI: 10.1016/j.jde.2022.02.052

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

Autores: Serena Guarino Lo Bianco; Domenico Angelo La Manna; Bozhidar Velichkov
Publicado en: Journal de l'Ecole polytechnique - Mathematiques, 2021, ISSN 2429-7100
Editor: Ecole polytechnique
DOI: 10.5802/jep.139

The regularity problem in domains with lower dimensional boundaries

Autores: Zanbing Dai; Joseph Feneuil; Svitlana Mayboroda
Publicado en: Journal of Functional Analysis, Edición 284, 2023, ISSN 0022-1236
Editor: Academic Press
DOI: 10.1016/j.jfa.2023.109903

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

Autores: Guy David, Joseph Feneuil, Svitlana Mayboroda
Publicado en: Mathematische Annalen, Edición 385, 2023, Página(s) 1797-1821, ISSN 0025-5831
Editor: Springer Verlag
DOI: 10.1007/s00208-022-02379-8

Second-order estimates for the p-Laplacian in RCD spaces

Autores: Luca Benatti, Ivan Yuri Violo
Publicado en: Journal of Differential Equations, Edición 439, 2025, Página(s) 113398, ISSN 0022-0396
Editor: Academic Press
DOI: 10.1016/j.jde.2025.113398

"Non-rigidity of the absolutely continuous part of <mml:math xmlns:mml=""http://www.w3.org/1998/Math/MathML"" altimg=""si1.svg""> <mml:mi mathvariant=""script"">A</mml:mi> </mml:math> -free measures"

Autores: Luigi De Masi, Carlo Gasparetto
Publicado en: Journal of Functional Analysis, Edición 289, 2025, Página(s) 111114, ISSN 0022-1236
Editor: Academic Press
DOI: 10.1016/j.jfa.2025.111114

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

Autores: Giulia Bevilacqua, Chiara Lonati
Publicado en: Bollettino dell'Unione Matematica Italiana, Edición 17, 2024, Página(s) 221-240, ISSN 1972-6724
Editor: Unione Matematica Italiana
DOI: 10.1007/s40574-023-00392-6

A vectorial problem with thin free boundary

Autores: Daniela De Silva, Giorgio Tortone
Publicado en: Calculus of Variations and Partial Differential Equations, Edición 62, 2023, ISSN 0944-2669
Editor: Springer Verlag
DOI: 10.1007/s00526-023-02561-z

Soap films: from the Plateau problem to deformable boundaries

Autores: Giulia Bevilacqua, Luca Lussardi, Alfredo Marzocchi
Publicado en: Communications in Applied and Industrial Mathematics, Edición 15, 2025, Página(s) 137-155, ISSN 2038-0909
Editor: Walter de Gruyter GmbH
DOI: 10.2478/caim-2024-0019

Regularity of the optimal sets for the second Dirichlet eigenvalue

Autores: Mazzoleni, Dario; Trey, Baptiste; Velichkov, Bozhidar
Publicado en: Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 2022, ISSN 0294-1449
Editor: Elsevier BV
DOI: 10.4171/aihpc/14

An epiperimetric inequality for odd frequencies in the thin obstacle problem

Autores: Matteo Carducci, Bozhidar Velichkov
Publicado en: Journal of Functional Analysis, Edición 289, 2025, Página(s) 111115, ISSN 0022-1236
Editor: Academic Press
DOI: 10.1016/j.jfa.2025.111115

Green functions and smooth distances

Autores: Joseph Feneuil, Linhan Li, Svitlana Mayboroda
Publicado en: Mathematische Annalen, Edición 389, 2024, Página(s) 2637-2727, ISSN 0025-5831
Editor: Springer Verlag
DOI: 10.1007/s00208-023-02715-6

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

Autores: François Générau; Édouard Oudet; Bozhidar Velichkov
Publicado en: Archive for Rational Mechanics and Analysis volume, Edición 246, 2022, Página(s) 561-602, ISSN 0003-9527
Editor: Springer Verlag
DOI: 10.1007/s00205-022-01821-0

Elastic membranes spanning deformable curves

Autores: Francesco Ballarin, Giulia Bevilacqua, Luca Lussardi, Alfredo Marzocchi
Publicado en: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Edición 104, 2024, ISSN 0044-2267
Editor: John Wiley & Sons Ltd.
DOI: 10.1002/zamm.202300890

Local multiplicity for fractional linear equations with Hardy potentials

Autores: Edoardo Mainini, Roberto Ognibene, Bruno Volzone
Publicado en: Calculus of Variations and Partial Differential Equations, Edición 64, 2025, ISSN 0944-2669
Editor: Springer Verlag
DOI: 10.1007/s00526-024-02914-2

On the isoperimetric Riemannian Penrose inequality

Autores: Luca Benatti, Mattia Fogagnolo, Lorenzo Mazzieri
Publicado en: Communications on Pure and Applied Mathematics, 2024, ISSN 0010-3640
Editor: John Wiley & Sons Inc.
DOI: 10.1002/cpa.22239

Quantitative spectral stability for Aharonov–Bohm operators with many coalescing poles

Autores: Veronica Felli, Benedetta Noris, Roberto Ognibene, Giovanni Siclari
Publicado en: Journal of the European Mathematical Society, 2025, ISSN 1435-9855
Editor: European Mathematical Society Publishing House
DOI: 10.4171/jems/1632

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

Autores: Guido De Philippis, Luca Spolaor, Bozhidar Velichkov
Publicado en: Inventiones Mathematicae, 2021, ISSN 1432-1297
Editor: Springer
DOI: 10.1007/s00222-021-01031-7

Carleson perturbations for the regularity problem

Autores: Zanbing Dai, Joseph Feneuil, Svitlana Mayboroda
Publicado en: Revista Matemática Iberoamericana, Edición 39, 2024, Página(s) 2119-2170, ISSN 0213-2230
Editor: Universidad Autonoma de Madrid
DOI: 10.4171/rmi/1401

Numerical computation of the cut locus <i>via</i> a variational approximation of the distance function

Autores: François Générau, Edouard Oudet, Bozhidar Velichkov
Publicado en: ESAIM: Mathematical Modelling and Numerical Analysis, Edición 56, 2022, Página(s) 105-120, ISSN 2822-7840
Editor: EDP Sciences
DOI: 10.1051/m2an/2021088

Vectorial Bernoulli Problems and Free Boundary Systems

Autores: Giorgio Tortone, Bozhidar Velichkov
Publicado en: La Matematica, Edición 5, 2026, ISSN 2730-9657
Editor: Springer Nature
DOI: 10.1007/s44007-026-00195-z

A variational analysis of nematic axisymmetric films: the covariant derivative case

Autores: G. Bevilacqua, C. Lonati, L. Lussardi, A. Marzocchi
Publicado en: Calculus of Variations and Partial Differential Equations, Edición 65, 2025, ISSN 0944-2669
Editor: Springer Verlag
DOI: 10.1007/s00526-025-03182-4

Shape optimization problems in control form

Autores: Giuseppe Buttazzo, Francesco Paolo Maiale, Bozhidar Velichkov
Publicado en: RENDICONTI LINCEI - MATEMATICA E APPLICAZIONI, 2021, ISSN 1120-6330
Editor: Accademia Nazionale dei Lincei
DOI: 10.4171/rlm/942

Regularity of minimal surfaces with capillary boundary conditions

Autores: Luigi De Masi, Nick Edelen, Carlo Gasparetto, Chao Li
Publicado en: Communications on Pure and Applied Mathematics, Edición 78, 2025, Página(s) 2436-2502, ISSN 0010-3640
Editor: John Wiley & Sons Inc.
DOI: 10.1002/cpa.70008

Higher Order Boundary Harnack Principle via Degenerate Equations

Autores: Susanna Terracini, Giorgio Tortone, Stefano Vita
Publicado en: Archive for Rational Mechanics and Analysis, Edición 248, 2024, ISSN 0003-9527
Editor: Springer Verlag
DOI: 10.1007/s00205-024-01973-1

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

Autores: Guido De Philippis, Luca Spolaor, Bozhidar Velichkov
Publicado en: Journal of the European Mathematical Society, 2024, ISSN 1435-9855
Editor: European Mathematical Society Publishing House
DOI: 10.4171/jems/1435

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

Autores: null null, Luca Benatti, null null, null null, Mattia Fogagnolo, null null, Lorenzo Mazzieri, null null
Publicado en: Symmetry, Integrability and Geometry: Methods and Applications, 2023, ISSN 1815-0659
Editor: 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

Autores: Francesco Paolo Maiale, Giorgio Tortone, Bozhidar Velichkov
Publicado en: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2022, ISSN 0391-173X
Editor: Stampacchia Guido
DOI: 10.2422/2036-2145.202112_003

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

Autores: Maria Colombo; Luca Spolaor; Bozhidar Velichkov
Publicado en: Interfaces and Free Boundaries, Edición 2, 2021, ISSN 1463-9963
Editor: European Mathematical Society Publishing House
DOI: 10.4171/ifb/452

On the spectrum of sets made of cores and tubes

Autores: Francesca Bianchi, Lorenzo Brasco, Roberto Ognibene
Publicado en: Journal of Convex Analysis, 2024, ISSN 0944-6532
Editor: Heldermann Verlag

A strong maximum principle for minimizers of the one-phase Bernoulli problem

Autores: Nick Edelen, Luca Spolaor, Bozhidar Velichkov
Publicado en: Indiana University Mathematics Journal, Edición 73, 2024, Página(s) 1061-1096, ISSN 0022-2518
Editor: Indiana University Press
DOI: 10.1512/iumj.2024.73.9922

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

Autores: Nick Edelen, Luca Spolaor, Bozhidar Velichkov
Publicado en: Calculus of Variations and Partial Differential Equations, Edición 63, 2024, ISSN 0944-2669
Editor: Springer Verlag
DOI: 10.1007/s00526-023-02610-7

On asymptotics of Robin eigenvalues in the Dirichlet limit

Autores: Roberto Ognibene
Publicado en: Communications in Partial Differential Equations, Edición 50, 2025, Página(s) 1174-1210, ISSN 0360-5302
Editor: Marcel Dekker Inc.
DOI: 10.1080/03605302.2025.2536098

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

Autores: Giulia Bevilacqua, Andrea Giorgini
Publicado en: SIAM Journal on Mathematical Analysis, Edición 56, 2024, Página(s) 6057-6120, ISSN 0036-1410
Editor: Society for Industrial and Applied Mathematics
DOI: 10.1137/23m1608902

Book chapters (2)

Geometric Invariants of Non-smooth Framed Curves

Autores: Giulia Bevilacqua, Luca Lussardi, Alfredo Marzocchi
Publicado en: Springer INdAM Series, Anisotropic Isoperimetric Problems and Related Topics, 2024, Página(s) 1-13
Editor: Springer Nature Singapore
DOI: 10.1007/978-981-97-6984-1_1

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

Autores: Luca Benatti, Mattia Fogagnolo
Publicado en: Springer INdAM Series, Anisotropic Isoperimetric Problems and Related Topics, 2024, Página(s) 169-199
Editor: Springer Nature Singapore
DOI: 10.1007/978-981-97-6984-1_8

Monographic books (1)

Regularity of the One-phase Free Boundaries

Autores: Bozhidar Velichkov
Publicado en: Lecture Notes of the Unione Matematica Italiana, 2023, ISBN 978-3-031-13237-7
Editor: Springer International Publishing
DOI: 10.1007/978-3-031-13238-4