Regularity of solutions of divergence form elliptic equations

Abstract:

The aim of this paper is to study local regularity in the Morrey spaces $L^{p,\lambda }$ of the first derivatives of the solutions of an elliptic second order equation in divergence form \begin{equation*} {\mathcal L} u \equiv -\sum _{i,j=1}^n (a_{ij}(x) u_{x_i})_{x_j} =div f(x)\quad \text {for a.a.} x\in \Omega , \end{equation*} where $f$ is assumed to be in some $L^{p,\lambda }$ spaces and the coefficients $a_{ij}$ belong to the space $VMO.$