Remark on a nonlocal isoperimetric problem

Vesa Julin

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arXiv · 1610.04449

Remark on a nonlocal isoperimetric problem

Vesa Julin

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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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Vesa Julin. 2016-10-14. Remark on a nonlocal isoperimetric problem. https://arxiv.org/abs/1610.04449

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