Regularity of solutions of divergence form elliptic equations

The aim of this paper is to study local regularity in the Morrey spaces L p , λ Lp,λ of the first derivatives of the solutions of an elliptic second order equation in divergence form L u ≡ − ∑ i , j = 1 n ( a i j ( x ) u x i ) x j = d i v f ( x ) for a.a. x ∈ Ω , {equation*} { L} u ≡ -∑ i,j=1^n (aᵢⱼ(x) ux_i)x_j =div f(x) for a.a. x∈ Ω , {equation*} where f f is assumed to be in some L p , λ Lp,λ spaces and the coefficients a i j aᵢⱼ belong to the space V M O . VMO.