Regularity of solutions of divergence form elliptic equations

Abstract

The aim of this paper is to study local regularity in the Morrey spaces Lp,λ of the first derivatives of the solutions of an elliptic second order equation in divergence form Lu ≡ − n ∑ i,j=1 (aij(x)uxi )xj = divf(x) for a.a. x ∈ Ω, where f is assumed to be in some Lp,λ spaces and the coefficients aij belong to the space V MO.