Time-dependent tug-of-war games and normalized parabolic $p$-Laplace equations

Jeongmin Han

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arXiv · 2011.05681

Time-dependent tug-of-war games and normalized parabolic $p$-Laplace equations

Jeongmin Han

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Abstract

This paper concerns 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 $T \to \infty$. 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.

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Jeongmin Han. 2020-11-11. Time-dependent tug-of-war games and normalized parabolic $p$-Laplace equations. https://arxiv.org/abs/2011.05681

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