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Optimal mass transportation and Mather theory

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Date
2007
Link to item file
http://hal.archives-ouvertes.fr/hal-00003587/en/
Dewey
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Sujet
Optimal transportation on manifolds; Lagrangian systems; Mather theory; Fathi's Weak KAM theory; Hamilton-Jacobi equations
Journal issue
Journal of the European Mathematical Society
Volume
9
Number
1
Publication date
2007
Article pages
85-121
Publisher
European Mathematical Society
DOI
http://dx.doi.org/10.4171/JEMS/74
URI
https://basepub.dauphine.fr/handle/123456789/788
Collections
  • CEREMADE : Publications
Metadata
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Author
Bernard, Patrick
Buffoni, Boris
Type
Article accepté pour publication ou publié
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.

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