Weak KAM pairs and Monge-Kantorovich duality
Dynamical Systems
2008-07-10 v2 Analysis of PDEs
Abstract
The dynamics of globally minimizing orbits of Lagrangian systems can be studied using the Barrier function, as Mather first did, or using the pairs of weak KAM solutions introduced by Fathi. The central observation of the present paper is that Fathi weak KAM pairs are precisely the admissible pairs for the Kantorovich problem dual to the Monge transportation problem with the Barrier function as cost. We exploit this observation to recover several relations between the Barrier functions and the set of weak KAM pairs in an axiomatic and elementary way.
Cite
@article{arxiv.math/0511746,
title = {Weak KAM pairs and Monge-Kantorovich duality},
author = {Patrick Bernard and Boris Buffoni},
journal= {arXiv preprint arXiv:math/0511746},
year = {2008}
}
Comments
Advanced Studies in Pure Mathematics 47, 2 (2007)