论文标题
与时期的拔河游戏和标准化的抛物线$ p $ -laplace方程式
Time-dependent tug-of-war games and normalized parabolic $p$-Laplace equations
论文作者
论文摘要
本文涉及与时间有关的拔河游戏的价值功能。我们首先证明价值功能的存在和独特性，并验证这些游戏值是否满足动态编程原理。在游戏值的存在证明中，我们还可以在$ t \ to \ infty $的情况下推断游戏值的渐近行为。此外，我们研究了游戏值的边界规律性。此后，根据价值函数的规律性结果，我们推断出游戏值会收敛到标准化抛物线$ p $ -laplace方程的粘度解决方案。
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.
