Weighed Estimates for Nonlinear Elliptic Problems with Orlicz Data

We study the Dirichlet problem for a divergence structure elliptic equation of p-Laplacian type that is not necessarily of variational form. A global maximal regularity is obtained for such a problem by proving that the gradient of the weak solution is as globally integrable as the nonhomogeneous term in weighted Orlicz spaces under minimal conditions on the nonlinearity and the domain. We find not only reasonable conditions imposed on the nonlinearity and the domain but also a correct relationship between the associated weight and Young function for such a weighted Orlicz regularity.