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Article Dans Une Revue Advanced Studies in Pure Mathematics. Année : 2007

Weak KAM pairs and Monge-Kantorovich duality

Résumé

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.
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Dates et versions

hal-00014963 , version 1 (30-11-2005)
hal-00014963 , version 2 (10-07-2008)

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Patrick Bernard, Boris Buffoni. Weak KAM pairs and Monge-Kantorovich duality. Advanced Studies in Pure Mathematics., 2007, Asymptotic analysis and singularities : elliptic and parabolic PDEs and related problems, 47 (2), pp.397-420. ⟨hal-00014963v2⟩
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