Weak KAM pairs and Monge-Kantorovich duality

Bernard, Patrick; Buffoni, Boris

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

Type

Communication / Conférence

External document link

http://hal.archives-ouvertes.fr/hal-00014963/en/

Date

2007

Conference title

14th MSJ International Research Institute "Asymptotic Analysis and Singularity"

Conference date

2005-07

Conference city

Sendai

Conference country

Japon

Book title

Asymptotic Analysis and Singularities: Elliptic and Parabolic PDEs and Related Problems

Book author

Yanagida, Eiji; Tsutsumi, Yoshio; Tanaka, Kazunaga; Kozono, Hideo

Publisher

AMS

Series title

Advanced Studies in Pure Mathematics

Series number

ISBN

978-4-931469-41-9

Number of pages

410

Pages

397-420

Metadata

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Author(s)

Bernard, Patrick

Buffoni, Boris

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 / Keywords

Minimizing measures; Monge-Kantorovich duality; Weak KAM theory