A result on the decay of the boundary layers in the homogenization theory

Abstract

Boundary layers are used in the homogenization of elliptic problems with periodically oscillating coefficients, for example when we want to improve the macroscopic approximation given by homogenization in the neighborhood of the boundary of a domain. For problems with a special geometry the boundary layers are defined on a semi‐infinite strip $]0,1[^{n-1}\times]0,\infty[\,$ , and their energies decrease exponentially with respect to the second variable.

In our paper, we show that in general this decay property does not hold, i.e., we cannot get uniform exponential decay of the boundary layers.