Time-dependent tug-of-war games and normalized parabolic p-Laplace equations. (January 2022)

• Record Type: Journal Article
• Authors: Han, Jeongmin
• Is Part Of: Nonlinear analysis. Volume 214(2022)
• Publication Date: 2022-01
• Subjects: primary 35K92 -- secondary 35K20 91A15; Dynamic programming principle -- Normalized p-Laplacian -- Stochastic games -- Tug-of-war -- Viscosity solutions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112542
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study value functions of time-dependent tug-of-war games. We first prove the existence and uniqueness of value functions and verify that these game values satisfy a dynamic programming principle. Using the arguments in the proof of existence of game values, we can also deduce asymptotic behavior of game values when T → ∞ . Furthermore, we investigate boundary regularity for game values. Thereafter, based on the regularity results for value functions, we deduce that game values converge to viscosity solutions of the normalized parabolic p -Laplace equation.