NON-HOMOGENEOUS CONORMAL DERIVATIVE PROBLEMS FOR DISCONTINUOUS QUASILINEAR ELLIPTIC EQUATIONS WITH MORREY DATA

A non-homogeneous conormal derivative problem is considered for quasilinear divergence form elliptic equations modeled on the m-Laplacian operator. The nonlinear terms are given by Carath´eodory functions and satisfy controlled growth structure conditions with respect to the solution and its gradient, while their x-behaviour is controlled in terms of suitable Morrey spaces. Global essential boundedness is proved for the weak solutions, generalizing thus the classical Lp-result of Ladyzhenskaya and Ural’tseva to the framework of the Morrey scales.