Some properties of an elliptic periodic problem with an interfacial resistance

Source abstract

Abstract In the homogenization of quasilinear elliptic problems, it is crucial for the homogenized matrix to have some kind of Lipschitz continuity in order to provide the uniqueness of the solution of the limit problem. In this paper, we prove that some estimates providing the uniqueness for a class of quasilinear problems in a periodic two‐component domain, remains valid after the homogenization process. To do that, we first prove a suitable Meyers type estimate for the periodic cell problem describing the homogenized matrix, which is posed in a two‐component cell, with a jump of the solution proportional to the flux prescribed on the interface. We also complete the study by a boundedness result for this periodic solution.