# Two dimensional optimal transportation problem for a distance cost with a convex constraint

Ping Chen; Feida Jiang; Xiaoping Yang

ESAIM: Control, Optimisation and Calculus of Variations (2013)

- Volume: 19, Issue: 4, page 1064-1075
- ISSN: 1292-8119

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topChen, Ping, Jiang, Feida, and Yang, Xiaoping. "Two dimensional optimal transportation problem for a distance cost with a convex constraint." ESAIM: Control, Optimisation and Calculus of Variations 19.4 (2013): 1064-1075. <http://eudml.org/doc/272802>.

@article{Chen2013,

abstract = {We first prove existence and uniqueness of optimal transportation maps for the Monge’s problem associated to a cost function with a strictly convex constraint in the Euclidean plane ℝ2. The cost function coincides with the Euclidean distance if the displacement y − x belongs to a given strictly convex set, and it is infinite otherwise. Secondly, we give a sufficient condition for existence and uniqueness of optimal transportation maps for the original Monge’s problem in ℝ2. Finally, we get existence of optimal transportation maps for a cost function with a convex constraint, i.e. y − x belongs to a given convex set with at most countable flat parts.},

author = {Chen, Ping, Jiang, Feida, Yang, Xiaoping},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {optimal transportation map; convex constraint; Monge transportation problem},

language = {eng},

number = {4},

pages = {1064-1075},

publisher = {EDP-Sciences},

title = {Two dimensional optimal transportation problem for a distance cost with a convex constraint},

url = {http://eudml.org/doc/272802},

volume = {19},

year = {2013},

}

TY - JOUR

AU - Chen, Ping

AU - Jiang, Feida

AU - Yang, Xiaoping

TI - Two dimensional optimal transportation problem for a distance cost with a convex constraint

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2013

PB - EDP-Sciences

VL - 19

IS - 4

SP - 1064

EP - 1075

AB - We first prove existence and uniqueness of optimal transportation maps for the Monge’s problem associated to a cost function with a strictly convex constraint in the Euclidean plane ℝ2. The cost function coincides with the Euclidean distance if the displacement y − x belongs to a given strictly convex set, and it is infinite otherwise. Secondly, we give a sufficient condition for existence and uniqueness of optimal transportation maps for the original Monge’s problem in ℝ2. Finally, we get existence of optimal transportation maps for a cost function with a convex constraint, i.e. y − x belongs to a given convex set with at most countable flat parts.

LA - eng

KW - optimal transportation map; convex constraint; Monge transportation problem

UR - http://eudml.org/doc/272802

ER -

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