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

Thierry Champion; Luigi De Pascale

Journal of the European Mathematical Society (2010)

- Volume: 012, Issue: 6, page 1355-1369
- ISSN: 1435-9855

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topChampion, 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 -

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