Linear and fully nonlinear elliptic equations with Morrey drift

Abstract

We present some results concerning the solvability of linear elliptic equations in bounded domains with the main coefficients almost in VMO, the drift and the free terms in Morrey classes containing $L_{d}$, and bounded zeroth order coefficient. We prove that the second-order derivatives of solutions are in a local Morrey class containing $W^{2}_{p,loc}$. Actually, the exposition is given for fully nonlinear equations and encompasses the above mentioned results, which are new even if the main part of the equation is just the Laplacian.