%0 Journal Article
%T An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus
%A Jianfeng Lu
%A Felix Otto
%J Mathematics
%D 2015
%I arXiv
%X We study an isoperimetric problem the energy of which contains the perimeter of a set, Coulomb repulsion of the set with itself, and attraction of the set to a background nucleus as a point charge with charge $Z$. For the variational problem with constrained volume $V$, our main result is that the minimizer does not exist if $V - Z$ is larger than a constant multiple of $\max(Z^{2/3}, 1)$. The main technical ingredients of our proof are a uniform density lemma and electrostatic screening arguments.
%U http://arxiv.org/abs/1508.07172v1