Geodesic
Optimal mass transportation and Mather theory
Journal of the European Mathematical Society, Tome 9 (2007) no. 1, pp. 85-121

Voir la notice de l'article provenant de la source EMS Press

We study the Monge transportation problem when the cost is the action associated to a Lagrangian function on a compact manifold. We show that the transportation can be interpolated by a Lipschitz lamination. We describe several direct variational problems the minimizers of which are these Lipschitz laminations. We prove the existence of an optimal transport map when the transported measure is absolutely continuous. We explain the relations with Mather's minimal measures.
DOI : 10.4171/jems/74
Classification : 49-XX, 00-XX
Keywords: 
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     author = {Patrick Bernard and Boris Buffoni},
     title = {Optimal mass transportation and {Mather} theory},
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}
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Patrick Bernard; Boris Buffoni. Optimal mass transportation and Mather theory. Journal of the European Mathematical Society, Tome 9 (2007) no. 1, pp. 85-121. doi: 10.4171/jems/74

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