H-convergence and homogenization of non-local elliptic operators in both perforated and non-perforated domains

摘要

We focus on the homogenization process of the non-local elliptic boundary value problem with 0 < s < 1, considering non-homogeneous Dirichlet-type condition outside of the bounded domain O subset of R-n. We find the homogenized coefficients as the standard H-limit of the sequence {A(epsilon)}(epsilon>0). We also prove that the commonly referred as the strange term does not appear in the homogenized problem associated with the fractional Laplace operator (-Delta)(s) in a perforated domain. Both of these results have been obtained in the class of general microstructures. This shows that the homogenization process, as epsilon -> 0, is stable under s -> 1(-) in the non-perforated domains, but not necessarily in the case of perforated domains.