Homogenization of a Nonlinear Elliptic Boundary Value Problem Modeling Galvanic Currents

We study a nonlinear elliptic boundary value problem arising from electrochemistry in the study of heterogeneous electrode surfaces. The boundary condition is of exponential type (Butler–Volmer) and has a periodic structure. We find a limiting or effective problem as the period approaches zero, along with a first order correction. We establish convergence estimates and provide numerical experiments.