Homogenization in polygonal domains

Abstract

We consider the homogenization of elliptic systems with $\epsilon$-periodic coefficients. Classical two-scale approximation yields a $O(\epsilon )$ error inside the domain. We discuss here the existence of higher order corrections, in the case of general polygonal domains. The corrector depends in a non-trivial way on the boundary. Our analysis extends substantially previous results obtained for polygonal domains with sides of rational slopes.