Geodesic
Optimal mass transportation and Mather theory
Journal of the European Mathematical Society, Tome 9 (2007) no. 1, pp. 85-121 Cet article a éte moissonné depuis la source EMS Press

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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},
     journal = {Journal of the European Mathematical Society},
     pages = {85--121},
     year = {2007},
     volume = {9},
     number = {1},
     doi = {10.4171/jems/74},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/74/}
}
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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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