Optimal mass transportation and Mather theory
Patrick Bernard
Université de Paris Dauphine, FranceBoris Buffoni
Ecole Polytechnique Federale, Lausanne, Switzerland
Abstract
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.
Cite this article
Patrick Bernard, Boris Buffoni, Optimal mass transportation and Mather theory. J. Eur. Math. Soc. 9 (2007), no. 1, pp. 85–121
DOI 10.4171/JEMS/74