Homogenization of the boundary value problem for the poisson equation with rapidly oscillating nonlinear boundary conditions: space dimension n ≥ 3, critical case

The homogenization of the Poisson equation in a bounded domain with rapidly oscillating boundary conditions specied on a part of the domain boundary is studied. A Neumann boundary condition alternates with an ε-periodically distributed nonlinear Robin condition involving the coefficient ε-β, where β ∈ R. The diameter of the boundary portions with a nonlinear Robin condition is of order O(εα), α > 1. A critical relation between the parameters α and β is considered