||Gradient estimates for double phase problems with irregular obstacles
||NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2018
||An irregular obstacle problem with non-uniformly elliptic operator in divergence form of (p, q)-growth is studied. We find an optimal regularity for such a double phase obstacle problem by essentially proving that the gradient of a solution is as integrable as both the gradient of the assigned obstacle function and the associated nonhomogeneous term in the divergence. Calderon-Zygmund type estimates are also obtained under minimal regularity requirements of the prescribed data. (C) 2018 Elsevier Ltd. All rights reserved.