Characterization of sets of finite local and non local perimeter via non local heat equation

TL;DR

This paper characterizes sets with finite local and non-local perimeters using $ ext{Gamma}$-convergence and applies this to prove the isoperimetric inequality in both cases.

Contribution

It introduces a $ ext{Gamma}$-convergence framework to characterize finite perimeter sets and proves the isoperimetric inequality for local and non-local perimeters.

Findings

Characterization of finite perimeter sets via $ ext{Gamma}$-convergence

Proof of the isoperimetric inequality in local and non-local cases

Framework applicable to both local and non-local perimeter problems

Abstract

In this paper we provide a characterization of sets of finite local and non local perimeter via a $\Gamma-$convergence result. As an application we give a proof of the isoperimetric inequality, both in the local and in the non local case.