Smooth critical sub-solutions of the Hamilton-Jacobi equation

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.

References in corpus (1)

• Weak KAM theorem on non compact manifolds

Cited by in corpus (1)

• Existence of $C^{1,1}$ critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds