Hessian estimates for fourth order elliptic systems with singular BMO coefficients in composite Reifenberg domains

Abstract

We consider fourth order elliptic systems in divergence form with greatly discontinuous coefficients in a nonsmooth domain. Our domain is composed of a finite number of disjoint subdomains with (δ,R)-Reifenberg flat boundaries, and the coefficients, which are allowed to have great discontinuity across the boundaries of subdomains, have small BMO semi-norms on each subdomain. Our main result is deriving the global W2,p (1<p<∞) regularity, with the estimates independent of the distance between the subdomains.