Mathematical Research Letters

Volume 14 (2007)

Number 3

Smooth critical sub-solutions of the Hamilton-Jacobi equation

Pages: 503 – 511

DOI: http://dx.doi.org/10.4310/MRL.2007.v14.n3.a14

Author

Patrick Bernard (Université de Paris Dauphine)

Abstract

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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