Upper-Bound Error Estimates for Double Phase Obstacle Problems with Clarke’s Subdifferential

Abstract

The main goal of this article is to investigate upper-bound error estimates (also called error bounds) for a class of double phase obstacle problems. We first recall double phase implicit obstacle problems involving Clarke’s subdifferential given by Zeng et al. [Calc. Var. Partial Differential Equations 59 (2020): 176]. Then, based on regularized gap functions introduced by Yamashita and Fukushima, we establish some regularized gap functions for the double phase obstacle problem. Finally, using the properties of Clarke’s subdifferential and double phase operators, the upper-bound error estimates for such double phase obstacle problems in terms of regularized gap functions are provided.