$H-$convergence result for nonlocal elliptic-type problems via Tartar's method

TL;DR

This paper establishes a compactness result for the $H$-convergence of nonlocal, nonlinear elliptic problems using Tartar's oscillating test functions method, advancing the understanding of their asymptotic behavior.

Contribution

It introduces a novel application of Tartar's method to nonlocal nonlinear elliptic problems, providing new compactness results for $H$-convergence.

Findings

Proves $H$-convergence compactness for nonlocal nonlinear elliptic problems

Extends Tartar's method to nonlocal operators

Provides theoretical foundation for homogenization of such problems

Abstract

In this work we obtain a compactness result for the $H-$convergence of a family of nonlocal and nonlinear monotone elliptic-type problems by means of Tartar's method of oscillating test functions.