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arXiv · 1003.2316

Pseudographs and Lax-Oleinik semi-group: a geometric and dynamical interpretation

Marie-Claude Arnaud
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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 (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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Marie-Claude Arnaud. 2010-07-01. Pseudographs and Lax-Oleinik semi-group: a geometric and dynamical interpretation. https://doi.org/10.1088/0951-7715%2F24%2F1%2F003

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