Remark on a nonlocal isoperimetric problem

2016/10/14 by Julin, Vesa
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1610.04449

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.

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