论文标题
Monge-Ampère的非线性平均价值属性
A Nonlinear Mean Value Property for Monge-Ampère
论文作者
论文摘要
近年来，人们对平均价值特性（已知表征谐波函数）是否可以以某种弱形式扩展到非线性方程解决方案的平均价值特性越来越兴趣。这个问题是由于几年前发现的随机拔河游戏与标准化的$ p- $ laplacian之间令人惊讶的联系所激发的，在这里，PDE解决方案的非线性渐近平均值属性与适当游戏的动态编程原理有关。目前，渐近非线性平均值公式在文献中很少见，我们的目标是表明经典的Monge-ampère方程中的渐近非线性平均值公式。
In recent years there has been an increasing interest in whether a mean value property, known to characterize harmonic functions, can be extended in some weak form to solutions of nonlinear equations. This question has been partially motivated by the surprising connection between Random Tug-of-War games and the normalized $p-$Laplacian discovered some years ago, where a nonlinear asymptotic mean value property for solutions of a PDE is related to a dynamic programming principle for an appropriate game. Currently, asymptotic nonlinear mean value formulas are rare in the literature and our goal is to show that an asymptotic nonlinear mean value formula holds for the classical Monge-Ampère equation.
