Mathematical Research Letters
Volume 14 (2007)
Smooth critical sub-solutions of the Hamilton-Jacobi equation
Pages: 503 – 511
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.