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arXiv · 2007.02107

Minimisers of a general Riesz-type Problem

Matteo Novaga·Aldo Pratelli
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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 $g:\mathbb R^N\setminus\{0\}\to \mathbb R^+$. 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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Matteo Novaga, Aldo Pratelli. 2021-03-18. Minimisers of a general Riesz-type Problem. https://arxiv.org/abs/2007.02107

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