Elliptic equations with BMO coefficients in Reifenberg domains

The inhomogeneous Dirichlet problems concerning divergence form elliptic equations are studied. Optimal regularity requirements on the coefficients and domains for the W^1,p theory, 1 < p < ∞, are obtained. The principal coefficients are supposed to be in the John‐Nirenberg space with small BMO seminorms. The domain is a Reifenberg domain. These conditions for the W^1,p theory not only weaken the requirements on the coefficients but also lead to a more general geometric condition on the domains. In fact, these domains might have fractal dimensions. © 2004 Wiley Periodicals, Inc.