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
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00003587/en/
Journal nameJournal of the European Mathematical Society
European Mathematical Society
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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 / KeywordsOptimal transportation on manifolds; Lagrangian systems; Mather theory; Fathi's Weak KAM theory; Hamilton-Jacobi equations
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