A generalization of a theorem by C. Miranda

Summary In this paper we study the well-posedness of the Dirichlet problem for an elliptic non divergence form second order equation. The coefficients are not assumed to be continuous but their derivatives are supposed to belong to a suitable Morrey space hence generalizing a classical result by C. Miranda.This work was partly financially supported by a national project of the Italian Ministero della Pubblica Istruzione and by G.N.A.F.A.-C.N.R.