论文标题
具有两个不同操作员（Laplacian和Infinity Laplacian）的椭圆系统的游戏理论方法
A game theoretical approach for an elliptic system with two different operators (the Laplacian and the infinity Laplacian)
论文作者
论文摘要
在本文中，我们通过概率方法找到了由两个不同的操作员（Laplacian和Infinity Laplacian）控制的椭圆系统的粘度解决方案。我们分析了一款将拔河比赛与两只不同公猪的随机步行相结合的游戏。我们表明，随着步骤大小为零，这些值函数均匀地收敛到椭圆系统的粘度解。 此外，我们使用纯PDE技术显示了椭圆系统的独特性。
In this paper we find viscosity solutions to an elliptic system governed by two different operators (the Laplacian and the infinity Laplacian) using a probabilistic approach. We analyze a game that combines the Tug-of-War with Random Walks in two different boars. We show that these value functions converge uniformly to a viscosity solution of the elliptic system as the step size goes to zero. In addition, we show uniqueness for the elliptic system using pure PDE techniques.
