The isoperimetric problem for nonlocal perimeters

2017/07/20 by Cesaroni, Annalisa, Novaga, Matteo · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1707.06504

Abstract

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.

Cited by

• Riesz fractional gradient functionals defined on partitions: nonlocal-to-local variational limits
• The Polya-Szego principle in the fractional setting: a glimpse on nonlocal functional inequalities

Related

• Isoperimetric problems for a nonlocal perimeter of Minkowski type
• A quantitative isoperimetric inequality for fractional perimeters
• Nonlocal isoperimetric inequalities for Kolmogorov-Fokker-Planck operators
• Isoperimetric inequality for nonlocal bi-axial discrete perimeter
• A nonlocal isoperimetric problem with density perimeter