Weak KAM pairs and Monge-Kantorovich duality
Bernard, Patrick; Buffoni, Boris (2007), Weak KAM pairs and Monge-Kantorovich duality, in Yanagida, Eiji; Tsutsumi, Yoshio; Tanaka, Kazunaga; Kozono, Hideo, Asymptotic Analysis and Singularities: Elliptic and Parabolic PDEs and Related Problems, AMS, p. 397-420
TypeCommunication / Conférence
External document linkhttp://hal.archives-ouvertes.fr/hal-00014963/en/
Conference title14th MSJ International Research Institute "Asymptotic Analysis and Singularity"
Book titleAsymptotic Analysis and Singularities: Elliptic and Parabolic PDEs and Related Problems
Book authorYanagida, Eiji; Tsutsumi, Yoshio; Tanaka, Kazunaga; Kozono, Hideo
Series titleAdvanced Studies in Pure Mathematics
Number of pages410
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Abstract (EN)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.
Subjects / KeywordsMinimizing measures; Monge-Kantorovich duality; Weak KAM theory
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