Nonlinear gradient estimates for generalized elliptic equations with nonstandard growth in nonsmooth domains

A generalized elliptic equation with nonstandard growth in a nonsmooth bounded domain is studied. A global nonlinear gradient estimate is obtained in the frame of Orlicz spaces under the assumptions that the associated Young functions satisfy some moderate growth and decay conditions and that the boundary of the domain is δδ-Reifenberg flat with δδ depending on the domain, the dimension of the domain and the Young functions.