On minimizers of an isoperimetric problem with long-range interactions under a convexity constraint
Résumé
We study a variational problem modeling the behavior at equilibrium of charged liquid drops under convexity constraint. After proving 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.
Origine : Fichiers produits par l'(les) auteur(s)
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