Irregular obstacle problems for Orlicz double phase

Abstract

An irregular obstacle problem with a non-uniformly elliptic operator in divergence form of (G,H)-growth is studied. We provide local Calderón-Zygmund type estimates for an Orlicz double phase problem by proving that the gradient of a solution is integrable as both the gradient of the obstacle function and the associated nonhomogeneous term in the divergence under sharp conditions on the nonlinearity.