Geodesic
The Monge problem for strictly convex norms in $\mathbb{R}^d$
Journal of the European Mathematical Society, Tome 12 (2010) no. 6, pp. 1355-1369.

Voir la notice de l'article provenant de la source EMS Press

We prove the existence of an optimal transport map for the Monge problem in a convex bounded subset of 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.
DOI : 10.4171/jems/234
Classification : 49-XX, 00-XX
Keywords: Monge–Kantorovich problem, optimal transport problem, cyclical monotonicity 
@article{JEMS_2010_12_6_a2,
     author = {Thierry Champion and Luigi De Pascale},
     title = {The {Monge} problem for strictly convex norms in $\mathbb{R}^d$},
     journal = {Journal of the European Mathematical Society},
     pages = {1355--1369},
     publisher = {mathdoc},
     volume = {12},
     number = {6},
     year = {2010},
     doi = {10.4171/jems/234},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/234/}
}
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Thierry Champion; Luigi De Pascale. The Monge problem for strictly convex norms in $\mathbb{R}^d$. Journal of the European Mathematical Society, Tome 12 (2010) no. 6, pp. 1355-1369. doi : 10.4171/jems/234. http://geodesic.mathdoc.fr/articles/10.4171/jems/234/

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