Geodesic
Two dimensional optimal transportation problem for a distance cost with a convex constraint
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 4, pp. 1064-1075 Cet article a éte moissonné depuis la source Numdam

Voir la notice de l'article

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.

DOI : 10.1051/cocv/2013045
Classification : 49Q20, 49J45
Keywords: optimal transportation map, convex constraint, Monge transportation problem 
@article{COCV_2013__19_4_1064_0,
     author = {Chen, Ping and Jiang, Feida and Yang, Xiaoping},
     title = {Two dimensional optimal transportation problem for a distance cost with a convex constraint},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1064--1075},
     year = {2013},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {4},
     doi = {10.1051/cocv/2013045},
     mrnumber = {3182681},
     zbl = {1282.49036},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013045/}
}
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
SP  - 1064
EP  - 1075
VL  - 19
IS  - 4
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013045/
DO  - 10.1051/cocv/2013045
LA  - en
ID  - COCV_2013__19_4_1064_0
ER  - 
%0 Journal Article
%A Chen, Ping
%A Jiang, Feida
%A Yang, Xiaoping
%T Two dimensional optimal transportation problem for a distance cost with a convex constraint
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2013
%P 1064-1075
%V 19
%N 4
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013045/
%R 10.1051/cocv/2013045
%G en
%F COCV_2013__19_4_1064_0
Chen, Ping; Jiang, Feida; Yang, Xiaoping. Two dimensional optimal transportation problem for a distance cost with a convex constraint. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 4, pp. 1064-1075. doi: 10.1051/cocv/2013045

Cité par Sources :