Stability of Ellipsoids as the Energy Minimizers of Perturbed Coulomb Energies

Joan Mateu; Maria Giovanna Mora; Luca Rondi; Lucia Scardia; Joan Verdera

doi:10.1137/22m1479695

Stability of Ellipsoids as the Energy Minimizers of Perturbed Coulomb Energies

Joan Mateu, Maria Giovanna Mora, Luca Rondi, Lucia Scardia, Joan Verdera

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Abstract

In this paper we characterize the minimizer for a class of nonlocal perturbations of the Coulomb energy. We show that the minimizer is the normalized characteristic function of an ellipsoid, under the assumption that the perturbation kernel has the same homogeneity as the Coulomb potential, is even, is smooth off the origin, and is sufficiently small. This result can be seen as the stability of ellipsoids as energy minimizers, since the minimizer of the Coulomb energy is the normalized characteristic function of a ball.

Original language	English
Pages (from-to)	3650-3676
Number of pages	27
Journal	SIAM Journal on Mathematical Analysis
Volume	55
Issue number	4
Early online date	18 Aug 2023
DOIs	https://doi.org/10.1137/22m1479695
Publication status	Published - Aug 2023

Keywords

Coulomb kernel
nonlocal interaction
potential theory

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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© 2023 Society for Industrial and Applied Mathematics.
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AU - Verdera, Joan

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Stability of Ellipsoids as the Energy Minimizers of Perturbed Coulomb Energies

Abstract

Keywords

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