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

Minimisers of a general Riesz-type problem

Novaga M.;Pratelli A.
2021-01-01

Abstract

We consider sets in RN which minimise, for fixed volume, the sum of the perimeter and a non-local term given by the double integral of a kernel g:RN∖{0}→R+. We establish some general existence and regularity results for minimisers. In the two-dimensional case we show that balls are the unique minimisers in the perimeter-dominated regime, for a wide class of functions g.
2021
Novaga, M.; Pratelli, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1114540
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