Nonlinear gradient estimates for double phase elliptic problems with irregular double obstacles

Abstract

An elliptic double phase problem with irregular double obstacles is investigated to establish a Calderón-Zygmund type estimate in the setting of Lebesgue spaces and weighted Lebesgue spaces. We prove that the gradient of a solution to such a highly nonlinear problem is as integrable as both the nonhomogeneous term in divergence form and the gradient of the associated double obstacles under minimal regularity requirements on the given nonlinear elliptic operator.