Optimal mass transportation and Mather theory

Bernard, Patrick, and Buffoni, Boris. "Optimal mass transportation and Mather theory." Journal of the European Mathematical Society 009.1 (2007): 85-121. <http://eudml.org/doc/277552>.

@article{Bernard2007,
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.},
author = {Bernard, Patrick, Buffoni, Boris},
journal = {Journal of the European Mathematical Society},
language = {eng},
number = {1},
pages = {85-121},
publisher = {European Mathematical Society Publishing House},
title = {Optimal mass transportation and Mather theory},
url = {http://eudml.org/doc/277552},
volume = {009},
year = {2007},
}

TY - JOUR
AU - Bernard, Patrick
AU - Buffoni, Boris
TI - Optimal mass transportation and Mather theory
JO - Journal of the European Mathematical Society
PY - 2007
PB - European Mathematical Society Publishing House
VL - 009
IS - 1
SP - 85
EP - 121
AB - 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.
LA - eng
UR - http://eudml.org/doc/277552
ER -