论文标题
通过Mather的平均功能，动作最小化集和弱KAM解决方案的属性
Properties of action-minimizing sets and weak KAM solutions via Mather's averaging functions
论文作者
论文摘要
我们从马瑟（Mather）平均功能方面研究了Tonelli Lagrangian和Hamiltony Systems的动作最小化不变套件的属性，以及Hamilton-Jacobi方程的弱KAM解决方案。我们的主要发现是，Mather的Alpha函数的暴露点和极端点与动作最小化不变式集合的分离属性和图形属性密切相关，这也与系统的集成性以及对汉密尔顿 - 雅各布方程的平滑弱KAM解决方案的存在有关。
We study properties of action-minimizing invariant sets for Tonelli Lagrangian and Hamiltonian systems and weak KAM solutions to the Hamilton-Jacobi equation in terms of Mather's averaging functions. Our principal discovery is that exposed points and extreme points of Mather's alpha function are closely related to disjoint properties and graph properties of the action-minimizing invariant sets, which is also related to $C^0$ integrability of the systems and the existence of smooth weak KAM solutions to the Hamilton-Jacobi equation.
