Elliptic equations with measurable coefficients in Reifenberg domains

Abstract

We prove W 1 , p estimates for elliptic equations in divergence form under the assumption that for each point and for each sufficiently small scale there is a coordinate system so that the coefficients have small oscillation in ( n − 1 ) directions. We assume the boundary to be δ-Reifenberg flat and the coefficients having small oscillation in the flat direction of the boundary.