Existence and stability for a non-local isoperimetric model of charged liquid drops
Analysis of PDEs
2014-07-17 v4
Abstract
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 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.
Keywords
Cite
@article{arxiv.1310.8217,
title = {Existence and stability for a non-local isoperimetric model of charged liquid drops},
author = {Michael Goldman and Matteo Novaga and Berardo Ruffini},
journal= {arXiv preprint arXiv:1310.8217},
year = {2014}
}