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

2015/08/28 by Jianfeng Lu, Félix Otto, Lu, Jianfeng +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Approximation and Integration #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1508.07172

openalex publication_date 2015/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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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