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 publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00003587/en/Date
2007Journal name
Journal of the European Mathematical SocietyVolume
9Number
1Publisher
European Mathematical Society
Pages
85-121
Publication identifier
Metadata
Show full item recordAbstract (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 equationsRelated items
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