Rigidity of the ball for an isoperimetric problem with strong capacitary repulsion

  • Michael Goldman

    Institut Polytechnique de Paris, Palaiseau, France
  • Matteo Novaga

    Università di Pisa, Pisa, Italy
  • Berardo Ruffini

    Università di Bologna, Bologna, Italy
Rigidity of the ball for an isoperimetric problem with strong capacitary repulsion cover

A subscription is required to access this article.

Abstract

We consider a variational problem involving competition between surface tension and charge repulsion. We show that, as opposed to the case of weak (short-range) interactions where we proved ill-posedness of the problem in a previous paper, when the repulsion is stronger the perimeter dominates the capacitary term at small scales. In particular, we prove existence of minimizers for small charges as well as their regularity. Combining this with the stability of the ball under small  perturbations, this ultimately leads to the minimality of the ball for small charges. We cover in particular the borderline case of the -capacity where both terms in the energy are of the same order.

Cite this article

Michael Goldman, Matteo Novaga, Berardo Ruffini, Rigidity of the ball for an isoperimetric problem with strong capacitary repulsion. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1451