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arXiv · 1508.07172

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

Jianfeng Lu·Felix Otto
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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.

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Jianfeng Lu, Felix Otto. 2015-08-28. An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus. https://arxiv.org/abs/1508.07172

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