Boundedness of the weak solutions to conormal problems for quasilinear elliptic equations with Morrey data

We consider a conormal problem for a class of quasilinear divergence form elliptic equations modeled on the m-Laplacian. The nonlinearities support controlled growths in the solution and its gradient, while their behaviour with respect to the independent variable is restrained in terms of Morrey spaces. We show global essential boundedness for the weak solutions, generalizing this way the classical L^p-result of Ladyzhenskaya and Ural’tseva to the settings of the Morrey spaces.