Calculus of Variations and Geometric Measure Theory

A. Cesaroni - M. Novaga

The isoperimetric problem for nonlocal perimeters

created by novaga on 20 Jul 2017
modified on 09 Nov 2018


Published Paper

Inserted: 20 jul 2017
Last Updated: 9 nov 2018

Journal: Discrete Contin. Dyn. Syst. S
Volume: 11
Number: 3
Pages: 425-440
Year: 2018

ArXiv: 1707.06504 PDF


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.