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

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.