Calculus of Variations and Geometric Measure Theory

M. Goldman - M. Novaga - B. Ruffini

Existence and stability for a non-local isoperimetric model of charged liquid drops

created by ruffini on 30 Oct 2013
modified by novaga on 03 Nov 2015


Published Paper

Inserted: 30 oct 2013
Last Updated: 3 nov 2015

Journal: Arch. Rat. Mech. Anal.
Volume: 217
Number: 1
Pages: 1-36
Year: 2015


We consider a variational problem related to the shape of charged liquid drops at equilibrium. We show that this problem never admits global minimizers with respect to L1 perturbations preserving the volume. This leads us to study it in more regular classes of competitors, for which we show existence of minimizers. We then prove that the ball is the unique solution for sufficiently small charges.