Global Weighted Gradient Estimates for Double Obstacle Problems with Orlicz Growth

Abstract

We study an irregular double obstacle problem with Orlicz growth on a bounded nonsmooth domain. The nonlinear operator is assumed to satisfy standard monotonicity and growth conditions, together with a small bounded mean oscillation condition in the spatial variable, while the domain is Reifenberg flat. We establish a global weighted Orlicz estimate for the gradient of the weak solution in terms of the nonhomogeneous datum, the gradients of the two obstacles, and the boundary datum.