Homogenization in oscillating boundary with non-homogeneous non-linear boundary conditions

Homogenization of an elliptic equation in a domain with oscillating boundary with non-homogeneous non-linear boundary conditions
We study a boundary value problem for the Laplacian in a domain, a part of whose boundary is highly oscillating (periodically), involving non-homogeneous non-linear Neumann or Robin boundary condition on the periodically oscillating boundary. Homogenization under non-homogeneous Neumann condition or the Robin boundary condition on an oscillating boundary has the induced difficulty of taking limits of surface integrals where the surface changes with respect to the parameter.