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arXiv · 2112.14136

Stability of ellipsoids as the energy minimisers of perturbed Coulomb energies

Joan Mateu·Maria Giovanna Mora·Luca Rondi·Lucia Scardia·Joan Verdera
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Abstract

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

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Joan Mateu, Maria Giovanna Mora, Luca Rondi, Lucia Scardia, Joan Verdera. 2021-12-28. Stability of ellipsoids as the energy minimisers of perturbed Coulomb energies. https://arxiv.org/abs/2112.14136

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