Periodic operators over a component domain and homogenization of some class of quasi-linear elliptic problems in two-component domain with interfacial resistance

TL;DR

This paper develops a homogenization framework for quasilinear elliptic PDEs in two-component domains with interfacial resistance, introducing a periodic extension operator to achieve strong convergence in Sobolev spaces.

Contribution

It presents a novel periodic extension operator and analyzes homogenization for two families of quasilinear elliptic problems with different data integrability.

Findings

Established strong convergence of function sequences in Sobolev spaces.

Derived homogenized equations for problems with L^2 and L^1 data.

Extended homogenization techniques to domains with interfacial resistance.

Abstract

This paper addresses the periodic homogenization of quasilinear elliptic PDEs in a two-component domain with an interfacial thermal barrier. It introduces a periodic extension operator that ensures strong convergence of function sequences in the Sobolev space. Moreover, two families of quasilinear elliptic problems in two-component domains with interfacial resistance will be considered here. One family with \(L^2\) data and another family with \(L^1\) data.