Stability of Ellipsoids as the Energy Minimizers of Perturbed Coulomb Energies

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

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
3 Downloads (Pure)


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 languageEnglish
Pages (from-to)3650-3676
Number of pages27
JournalSIAM Journal on Mathematical Analysis
Issue number4
Early online date18 Aug 2023
Publication statusPublished - Aug 2023


  • Coulomb kernel
  • nonlocal interaction
  • potential theory

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this