Boundary layer effects in homogenization

Understanding the contributions of boundary layers is important in many quantitative homogenization problems: In stochastic homogenization, boundary layer effects impact the accuracy of representative volume approximations for effective material properties. In both periodic and stochastic homogenization, the derivation of higher-order homogenized approximations on bounded domains necessitates an understanding of the homogenization problem for fluctuating boundary data. We give an overview of recent progress on the analysis of boundary layers for elliptic homogenization problems, including in particular decay estimates for boundary layers for random elliptic operators.

based on joint works with Peter Bella, Marc Josien, Claudia Raithel