Mathematical Research Letters

Volume 14, Issue 3, May 2007 pp. 503-511.

Smooth critical sub-solutions of the Hamilton-Jacobi equation

Authors: Patrick Bernard
Author institution: Université de Paris Dauphine

Summary: We establish the existence of smooth critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds for smooth convex Hamiltonians, that is in the context of weak KAM theory, under the assumption that the Aubry set is the union of finitely many hyperbolic periodic orbits or fixed points.

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