Minimisers of a general Riesz-type Problem

2020/07/04 by Novaga, Matteo, Pratelli, Aldo · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2007.02107

Abstract

We consider sets in \mathbb R^N which minimise, for fixed volume, the sum of the perimeter and a non-local term given by the double integral of a kernel g:\mathbb R^N∖\0\→ \mathbb R⁺. We establish some general existence and regularity results for minimisers. In the two-dimensional case we show that balls are the unique minimisers if the perimeter-dominated regime, for a wide class of functions g.

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• Existence and nonexistence results for a nonlocal isoperimetric problem on ℍⁿ

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