Journal of the European Mathematical Society
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Optimal mass transportation and Mather theoryPatrick Bernard and Boris Buffoni (1) Université de Paris Dauphine, France
(2) Ecole Polytechnique Federale, Lausanne, Switzerland
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.
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Bernard Patrick, Buffoni Boris: Optimal mass transportation and Mather theory. J. Eur. Math. Soc. 9 (2007), 85-121. doi: 10.4171/JEMS/74