Homogenization of nonlinear equations with mixed boundary conditions

Abstract

In this paper, we will study the convergence rates of solutions for homogenization of quasilinear elliptic equations with the mixed Dirichlet-Robin boundary conditions. Thanks to the smoothing operator as well as homogenization tools, we could handle the different boundary conditions in a uniform fashion. As a consequence, we establish the sharp rates of convergence in H1 and L2, which may be regarded as an extension from the classical linear equations Dirichlet or Neumann problems to a nonlinear case with the mixed boundary settings.