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.

Keywords:

• Clarke’s subdifferential
• double phase obstacle problem
• double phase operator
• error estimate
• regularized gap function
• upper bound

AMS CLASSIFICATION:

• 35J20
• 35J60

Acknowledgment

I would like to express my sincere gratitude to the two anonymous referees for their careful reading of the article and favorable comments.

Additional information

Funding

This research was supported by Ministry of Education and Training of Vietnam under Grant Number B2021.SPD.03.