Pseudographs and Lax-Oleinik semi-group: a geometric and dynamical interpretation
Symplectic Geometry
2015-05-18 v2 Dynamical Systems
Abstract
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 (\phi t) the Hamiltonian flow of H, we prove that for t > 0 small enough, \phi-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.
Cite
@article{arxiv.1003.2316,
title = {Pseudographs and Lax-Oleinik semi-group: a geometric and dynamical interpretation},
author = {Marie-Claude Arnaud},
journal= {arXiv preprint arXiv:1003.2316},
year = {2015}
}