Interior Estimates in Morrey Spaces for Strong Solutions to Nondivergence Form Equations with Discontinuous Coefficients

Let us consider the nondivergence form elliptic equation aijuxixj = ƒ In this paper we show that if the known term ƒ belongs to the Morrey space Lp, λ then the second derivatives of the W2, p-solution u belong to the same space. Next we derive a C1, αloc-regularity result that is related to a recent work by Caffarelli.