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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.