Bounds in spaces of Morrey under Cordes type conditions

In the study of boundary value problems for linear elliptic equations in nondivergence form with discontinuous coefficients we consider the class of discontinuity of Cordes type. In particular we state some local and non local a priori bounds for solutions of Dirichlet problem in unbounded domains. The coefficients of lower terms in the differential operator belong to Morrey spaces and the principal coefficients are 'near' to functions satisfying a condition of Cordes type. Our results are based on embedding theorems which allow us to require a summability lower than n for the coefficients of the operator L. We introduce a modulus of continuity of the functions in Morrey spaces to obtain the dependence of the constants in the estimates. We state also a result about the multiplication operator from W^1(\Omega) in L^2(\Omega)