Non-local functionals, total variation, and Gamma-convergence with respect to area-strict convergence

TL;DR

This paper investigates a class of non-local functionals related to total variation, establishing their Gamma-limit with respect to area-strict convergence, which advances understanding of variational convergence in this context.

Contribution

The paper determines the Gamma-limit of non-local functionals characterizing total variation under area-strict convergence, extending previous theoretical frameworks.

Findings

Gamma-limit of non-local functionals identified

Results connect non-local functionals to total variation

Advances in variational convergence theory

Abstract

We study a class of non-local functionals that was introduced by Brezis--Seeger--Van Schaftingen--Yung, and can be used to characterize the total variation of functions. We establish the $\Gamma$-limit of these functionals with respect to area-strict convergence.