Titre :

Uniform $C^{1,\alpha}$-regularity for almost-minimizers of some nonlocal perturbations of the perimeter

Auteur(s) :

Goldman, Michael [Auteur]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
Institut Polytechnique de Paris [IP Paris]
Merlet, Benoît [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Pegon, Marc [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Titre de la revue :

Archive for Rational Mechanics and Analysis

Pagination :

102

Éditeur :

Springer Verlag

Date de publication :

2024-10-22

ISSN :

0003-9527

Mot(s)-clé(s) en anglais :

geometric variational problems
nonlocal isoperimetric problems
nonlocal perimeters
regularity
liquid drop model

Discipline(s) HAL :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Optimisation et contrôle [math.OC]
Mathématiques [math]/Physique mathématique [math-ph]

Résumé en anglais : [en]

In this paper, we establish a $C^{1,\alpha}$-regularity theorem for almost-minimizers of the functional $\mathcal{F}_{\varepsilon,\gamma}=P-\gamma P_{\varepsilon}$, where $\gamma\in(0,1)$ and $P_{\varepsilon}$ is a nonlocal ...
Lire la suite >In this paper, we establish a $C^{1,\alpha}$-regularity theorem for almost-minimizers of the functional $\mathcal{F}_{\varepsilon,\gamma}=P-\gamma P_{\varepsilon}$, where $\gamma\in(0,1)$ and $P_{\varepsilon}$ is a nonlocal energy converging to the perimeter as $\varepsilon$ vanishes.Our theorem provides a criterion for $C^{1,\alpha}$-regularity at a point of the boundary which is uniform as the parameter $\varepsilon$ goes to $0$.As a consequence we obtain that volume-constrained minimizers of $\mathcal{F}_{\varepsilon,\gamma}$ are balls for any $\varepsilon$ small enough. For small $\varepsilon$, this minimization problem corresponds to the large mass regime for a Gamow-type problem where the nonlocal repulsive term is given by an integrable kernel $G$ with sufficiently fast decay at infinity.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Optimisation de forme

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL