Calculus of Variations and Geometric Measure Theory
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A. Cesaroni - M. Novaga

The isoperimetric problem for nonlocal perimeters

created by novaga on 20 Jul 2017
modified on 03 Sep 2017


Accepted Paper

Inserted: 20 jul 2017
Last Updated: 3 sep 2017

Journal: Discrete Contin. Dyn. Syst. S
Year: 2017


We consider a class of nonlocal generalized perimeters which includes fractional perimeters and Riesz type potentials. We prove a general isoperimetric inequality for such functionals, and we discuss some applications. In particular we prove existence of an isoperimetric profile, under suitable assumptions on the interaction kernel.


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