Weak KAM theorem on non compact manifolds

Abstract

In this paper, we consider a time independent $C^2$ Hamiltonian, sa\-tisfying the usual hypothesis of the classical Calculus of Variations, on a non-compact connected manifold. Using the Lax-Oleinik semigroup, we give a proof of the existence of weak KAM solutions, or viscosity solutions, for the associated Hamilton-Jacobi Equation. This proof works also in presence of symmetries. We also study the role of the amenability of the group of symmetries to understand when the several critical values that can be associated with the Hamiltonian coincide.

arXiv admin note: text overlap with arXiv:1004.0086 by other authors

Cited by in corpus (6)

• On weak KAM theory for N-body problems
• Min-max representations of viscosity solutions of Hamilton-Jacobi equations and applications in rare-event simulation
• On the stability of Mañé critical hypersurfaces
• On a theorem due to Birkhoff
• Mather problem and viscosity solutions in the stationary setting
• Invariance of global solutions of the Hamilton-Jacobi equation