Global gradient estimates for non-uniformly elliptic equations

We consider a nonlinear and non-uniformly elliptic problem in divergence form on a bounded domain. The problem under consideration is characterized by the fact that its ellipticity rate and growth radically change with the position, which provides a model for describing a feature of strongly anisotropic materials. We establish the global Calderón–Zygmund type estimates for the distributional solution in the case that the boundary of the domain is of class \(C^{1,\beta }\) for some \(\beta >0\).