Weak KAM theorem on non compact manifolds
Dynamical Systems
2015-02-24 v1
Abstract
In this paper, we consider a time independent 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.
Cite
@article{arxiv.1502.06247,
title = {Weak KAM theorem on non compact manifolds},
author = {Albert Fathi and Ezequiel Maderna},
journal= {arXiv preprint arXiv:1502.06247},
year = {2015}
}
Comments
arXiv admin note: text overlap with arXiv:1004.0086 by other authors