An Extension of the Aleksandrov]Pucci Theorem for Unbounded Domains

In this paper we extend a well-known a priori bound by Aleksandrov and Pucci for the solution of the Dirichlet problem for a uniformly elliptic operator in nonvariational form with discontinuous coefficients in a bounded open subset V of Rn to the case V is unbounded, under the assumption that the solution satisfies a suitable condition at infinity.