Application of potential estimates to a priori bounds for elliptic equations

Some a priori bounds for the solutions of certain classes of Dirichlet problems associated to non divergence structure elliptic equations will be presented, both under the Cordes condition and under a more general hypothesis [1, 2]. The estimates are achieved thanks to a potential esti- mate obtained for the solutions of the same kind of problems, but with more regular datum. References [1] F. Mamedov, S. Monsurrò, M. Transirico, Potential estimates and a priori estimates for elliptic equations, submitted. [2] F. Mamedov, S. Monsurrò, M. Transirico, Potential estimates and applications to elliptic equations, to appear on Discrete Contin. Dyn. Syst. Ser. S.