An extension theorem from connected sets and homogenization of non-local functionals

TL;DR

This paper investigates the asymptotic behavior of convolution-type functionals on periodic domains, establishing an extension theorem that advances understanding in homogenization of non-local functionals.

Contribution

It introduces a new extension theorem for connected sets, facilitating the analysis of homogenization in non-local functional problems.

Findings

Proved an extension theorem for connected sets.

Analyzed asymptotic behavior of convolution-type functionals.

Enhanced methods for homogenization of non-local functionals.

Abstract

We study the asymptotic behaviour of convolution-type functionals defined on general periodic domains by proving an extension theorem