Homogenization of a nonlinear elliptic problem with imperfect rough interface

Abstract

This paper deals with an elliptic problem with a nonlinear lower order term set in an open bounded cylinder of $R^N$, $N\geq 2$, divided into two connected components by an imperfect rough interface. More precisely, we assume that at the interface the flux is continuous and proportional, via a nonlinear rule, to the jump of the solution. According to the amplitude of the interface oscillations and the proportionality coefficient, we derive different homogenized problems.