Global gradient estimates for asymptotically regular problems of p (x) -Laplacian type

We study an asymptotically regular problem of p(x)-Laplacian type with discontinuous nonlinearity in a nonsmooth bounded domain. A global Calderón-Zygmund estimate is established for such a nonlinear elliptic problem with nonstandard growth under the assumption that the associated nonlinearity has a more general kind of the asymptotic behavior near the infinity with respect to the gradient variable. We also address an optimal regularity requirement on the nonlinearity as well as a minimal geometric assumption on the boundary of the domain for the nonlinear Calderón-Zygmund theory in the setting of variable exponent Sobolev spaces.