The Monge problem in ${\mathbb R}^d$
Champion, Thierry ; De Pascale, Luigi
Duke Math. J., Tome 156 (2011) no. 1, p. 551-572 / Harvested from Project Euclid
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We first consider the Monge problem in a convex bounded subset of ${\mathbb R}^d$ . The cost is given by a general norm, and we prove the existence of an optimal transport map under the classical assumption that the first marginal is absolutely continuous with respect to the Lebesgue measure. In the final part of the paper we show how to extend this existence result to a general open subset of ${\mathbb R}^d$ .
Publié le : 2011-04-15
Classification:  49J45,  49K30,  49Q20 
@article{1301678733,
     author = {Champion, Thierry and De Pascale, Luigi},
     title = {The Monge problem in ${\mathbb R}^d$},
     journal = {Duke Math. J.},
     volume = {156},
     number = {1},
     year = {2011},
     pages = { 551-572},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1301678733}
}

Champion, Thierry; De Pascale, Luigi. The Monge problem in ${\mathbb R}^d$. Duke Math. J., Tome 156 (2011) no. 1, pp.  551-572. http://gdmltest.u-ga.fr/item/1301678733/