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Optimal mass transportation and Mather theory

Bernard, Patrick; Buffoni, Boris (2007), Optimal mass transportation and Mather theory, Journal of the European Mathematical Society, 9, 1, p. 85-121. http://dx.doi.org/10.4171/JEMS/74

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00003587/en/
Date
2007
Journal name
Journal of the European Mathematical Society
Volume
9
Number
1
Publisher
European Mathematical Society
Pages
85-121
Publication identifier
Metadata
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Author(s)
Bernard, Patrick cc
Buffoni, Boris
Abstract (EN)
We study optimal transportation of measures on compact manifolds for costs defined from convex Lagrangians. We prove that optimal transportation can be interpolated by measured Lipschitz laminations, or geometric currents. The methods are inspired from Mather theory on Lagrangian systems. We make use of viscosity solutions of the associated Hamilton-Jacobi equation in the spirit of Fathi's approach to Mather theory.
Subjects / Keywords
Optimal transportation on manifolds; Lagrangian systems; Mather theory; Fathi's Weak KAM theory; Hamilton-Jacobi equations