An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus

Abstract

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.

28 pages, 3 figures

References in corpus (1)

• Minimality via second variation for a nonlocal isoperimetric problem

Cited by in corpus (1)

• Ground-states for the liquid drop and TFDW models with long-range attraction