Global gradient estimates for a general class of quasilinear elliptic equations with Orlicz growth

Abstract

We provide an optimal global Calderón-Zygmund theory for quasilinear elliptic equations of a very general form with Orlicz growth on bounded nonsmooth domains under minimal regularity assumptions of the nonlinearity A = A ( x , u , D u ) A=A(x,u,Du) in the first and second variables ( x , z ) (x,z) as well as on the boundary of the domain. Our result improves known regularity results in the literature regarding nonlinear elliptic operators depending on a given bounded weak solution.