伪图与Lax-Oleinik半群：一个几何和动力学解释
Pseudographs and Lax-Oleinik semi-group: a geometric and dynamical interpretation
摘要：
设H是定义在紧致连通流形余切丛上的Tonelli Hamilton算子，u是定义在M上的半凹函数.设E（u）是u的所有超微分的集合，（t）是H的Hamilton流，证明了当t > 0足够小时，（t）-t（E（u））是一个正合Lagrangian Lipschitz图.这提供了由P.~引入的正则化工具的几何解释/解释。Bernard证明了C1，1子解的存在性.
英文摘要：
Let H be a Tonelli Hamiltonian defined on the cotangent bundle of a compact and connected manifold and let u be a semi-concave function defined on M. If E (u) is the set of all the super-differentials of u and (ϕt) the Hamiltonian flow of H, we prove that for t > 0 small enough, ϕ-t (E (u)) is an exact Lagrangian Lipschitz graph. This provides a geometric interpretation/explanation of a regularization tool that was introduced by P.~Bernard to prove the existence of C 1,1 subsolutions.
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