Homogenization of a nonlinear monotone problem in a locally periodic domain via unfolding method

In this paper, the asymptotic behavior of the solutions of a monotone problem posed in a locally periodic oscillating domain is studied. Nonlinear monotone boundary conditions are imposed on the oscillating part of the boundary whereas the Dirichlet condition is considered on the smooth separate part. Using the unfolding method, under natural hypothesis on the regularity of the domain, we prove the weak L-p-convergence of the zero-extended solutions of the nonlinear problem and their flows to the solutions of a limit distributional problem. (C) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper studies the asymptotic behavior of the solutions of a monotone problem posed in a locally periodic oscillating domain. Nonlinear monotone boundary conditions are imposed on the oscillating part of the boundary, while the Dirichlet condition is considered on the smooth separate part. By using the unfolding method and making natural hypotheses on the regularity of the domain, we prove the weak L-p-convergence of the zero-extended solutions of the nonlinear problem and their flows to the solutions of a limit distributional problem.