Published Paper
Inserted: 9 jul 2020
Last Updated: 29 mar 2021
Journal: Nonlinear Analysis
Volume: 209
Number: 112346
Year: 2021
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 $g : \mathbb R^N\setminus\{0\}→\mathbb R^+$. 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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