Weak KAM pairs and Monge-Kantorovich duality

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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.
Advanced Studies in Pure Mathematics 47, 2 (2007)

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Dynamical Systems, Analysis of PDEs, 37J50; 49L25; 90C46

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http://salesiana.dossiersoluciones.com/handle/123456789/164591

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0511746
 http://arxiv.org/abs/math/0511746

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arXiv