The Monge problem for strictly convex norms in ${ℝ}^d$

Champion, Thierry, and De Pascale, Luigi. "The Monge problem for strictly convex norms in $\mathbb {R}^d$." Journal of the European Mathematical Society 012.6 (2010): 1355-1369. <http://eudml.org/doc/277257>.

@article{Champion2010,
abstract = {We prove the existence of an optimal transport map for the Monge problem in a convex bounded subset of $\mathbb \{R\}^d$ under the assumptions that the first marginal is absolutely continuous with respect to the Lebesgue measure and that the cost is given by a strictly convex norm. We propose a new approach which does not use disintegration of measures.},
author = {Champion, Thierry, De Pascale, Luigi},
journal = {Journal of the European Mathematical Society},
keywords = {Monge–Kantorovich problem; optimal transport problem; cyclical monotonicity; Monge-Kantorovich problem; optimal transport problem; cyclical monotonicity},
language = {eng},
number = {6},
pages = {1355-1369},
publisher = {European Mathematical Society Publishing House},
title = {The Monge problem for strictly convex norms in $\mathbb \{R\}^d$},
url = {http://eudml.org/doc/277257},
volume = {012},
year = {2010},
}

TY - JOUR
AU - Champion, Thierry
AU - De Pascale, Luigi
TI - The Monge problem for strictly convex norms in $\mathbb {R}^d$
JO - Journal of the European Mathematical Society
PY - 2010
PB - European Mathematical Society Publishing House
VL - 012
IS - 6
SP - 1355
EP - 1369
AB - We prove the existence of an optimal transport map for the Monge problem in a convex bounded subset of $\mathbb {R}^d$ under the assumptions that the first marginal is absolutely continuous with respect to the Lebesgue measure and that the cost is given by a strictly convex norm. We propose a new approach which does not use disintegration of measures.
LA - eng
KW - Monge–Kantorovich problem; optimal transport problem; cyclical monotonicity; Monge-Kantorovich problem; optimal transport problem; cyclical monotonicity
UR - http://eudml.org/doc/277257
ER -