Abstract.
In this paper, we consider a time independent C2 Hamiltonian, satisfying 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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fathi, A., Maderna, E. Weak kam theorem on non compact manifolds. Nonlinear differ. equ. appl. 14, 1–27 (2007). https://doi.org/10.1007/s00030-007-2047-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00030-007-2047-6