Uniform $C^{1,\alpha}$-regularity for almost-minimizers of some nonlocal perturbations of the perimeter - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

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

Résumé

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 \textsl{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.
Fichier principal
Vignette du fichier
uniform_regularity_hal2.pdf (733.13 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03623418 , version 1 (29-03-2022)
hal-03623418 , version 2 (16-08-2022)
hal-03623418 , version 3 (22-09-2022)

Identifiants

  • HAL Id : hal-03623418 , version 2

Citer

Michael Goldman, Benoît Merlet, Marc Pegon. Uniform $C^{1,\alpha}$-regularity for almost-minimizers of some nonlocal perturbations of the perimeter. 2022. ⟨hal-03623418v2⟩
206 Consultations
76 Téléchargements

Partager

Gmail Facebook X LinkedIn More