W1,p ESTIMATES FOR ELLIPTIC SYSTEMS ON COMPOSITE MATERIAL WITH ALMOST PARTIALLY BMO COEFFICIENTS

In this paper, we establish uniform W-1,W-p estimates for composite material problems which can be described by a divergence form elliptic system on a nonsmooth domain composed of a finite number of subdomains. We want to derive global W-1,W-p regularity under the assumption that the coefficients are almost (delta, R)-vanishing of codimension 1 (see Definition 1.2) in each of multiple subdomains and the boundaries of subdomains are Reifenberg flat, moreover the estimates do not depend on the distance between these subdomains.