On minimizers of an isoperimetric problem with long-range interactions under a convexity constraint

Michael Goldman; Matteo Novaga; Berardo Ruffini

doi:10.2140/apde.2018.11.1113

On minimizers of an isoperimetric problem with long-range interactions under a convexity constraint

Michael Goldman
, Matteo Novaga
, Berardo Ruffini

Laboratoire de Probabilités et Modèles Aléatoires
University of Pisa
Université de Montpellier 2

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

12 Citations (Scopus)

Résumé

We study a variational problem modeling the behavior at equilibrium of charged liquid drops under a convexity constraint. After proving the well-posedness of the model, we show C^1,1-regularity of minimizers for the Coulombic interaction in dimension two. As a by-product we obtain that balls are the unique minimizers for small charge. Eventually, we study the asymptotic behavior of minimizers, as the charge goes to infinity.

langue originale	Anglais
Pages (de - à)	1113-1142
Nombre de pages	30
journal	Analysis and PDE
Volume	11
Numéro de publication	5
Les DOIs	https://doi.org/10.2140/apde.2018.11.1113
état	Publié - 1 janv. 2018
Modification externe	Oui

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10.2140/apde.2018.11.1113

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abstract = "We study a variational problem modeling the behavior at equilibrium of charged liquid drops under a convexity constraint. After proving the well-posedness of the model, we show C1,1-regularity of minimizers for the Coulombic interaction in dimension two. As a by-product we obtain that balls are the unique minimizers for small charge. Eventually, we study the asymptotic behavior of minimizers, as the charge goes to infinity.",

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AB - We study a variational problem modeling the behavior at equilibrium of charged liquid drops under a convexity constraint. After proving the well-posedness of the model, we show C1,1-regularity of minimizers for the Coulombic interaction in dimension two. As a by-product we obtain that balls are the unique minimizers for small charge. Eventually, we study the asymptotic behavior of minimizers, as the charge goes to infinity.

KW - Convexity constraint

KW - Nonlocal isoperimetric problem

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On minimizers of an isoperimetric problem with long-range interactions under a convexity constraint

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