English

Remark on a nonlocal isoperimetric problem

Analysis of PDEs 2016-10-17 v1

Abstract

We consider isoperimetric problem with a nonlocal repulsive term given by the Newtonian potential. We prove that regular critical sets of the functional are analytic. This optimal regularity holds also for critical sets of the Ohta-Kawasaki functional. We also prove that when the strength of the nonlocal part is small the ball is the only possible stable critical set.

Keywords

Cite

@article{arxiv.1610.04449,
  title  = {Remark on a nonlocal isoperimetric problem},
  author = {Vesa Julin},
  journal= {arXiv preprint arXiv:1610.04449},
  year   = {2016}
}
R2 v1 2026-06-22T16:20:52.893Z