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}
}