Homogenization of Neumann boundary data with fully nonlinear operator
Sunhi Choi, Inwon Kim, Ki-Ahm Lee · Analysis & PDE · 2013
In this paper we study periodic homogenization problems for solutions of fully nonlinear PDEs in half-spaces with oscillatory Neumann boundary data.We show the existence and uniqueness of the homogenized Neumann data for a given half-space.Moreover, we show that there exists a continuous extension of the homogenized slope as the normal of the half-space varies over "irrational" directions.With F, g and ν as given above, our goal is to describe the limiting behavior of u ε as ε → 0, where