An optimal matching problem

@article{Ekeland2005,
abstract = {Given two measured spaces $(X,\mu )$ and $(Y,\nu )$, and a third space $Z$, given two functions $u(x,z)$ and $v(x,z)$, we study the problem of finding two maps $s:X\rightarrow Z$ and $t:Y\rightarrow Z$ such that the images $s(\mu )$ and $t(\nu )$ coincide, and the integral $\int _\{X\}u(x,s(x))d\mu -\int _\{Y\}v(y,t(y))d\nu $ is maximal. We give condition on $u$ and $v$ for which there is a unique solution.},
author = {Ekeland, Ivar},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {optimal transportation; measure-preserving maps},
language = {eng},
number = {1},
pages = {57-71},
publisher = {EDP-Sciences},
title = {An optimal matching problem},
url = {http://eudml.org/doc/246109},
volume = {11},
year = {2005},
}

TY - JOUR
AU - Ekeland, Ivar
TI - An optimal matching problem
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2005
PB - EDP-Sciences
VL - 11
IS - 1
SP - 57
EP - 71
AB - Given two measured spaces $(X,\mu )$ and $(Y,\nu )$, and a third space $Z$, given two functions $u(x,z)$ and $v(x,z)$, we study the problem of finding two maps $s:X\rightarrow Z$ and $t:Y\rightarrow Z$ such that the images $s(\mu )$ and $t(\nu )$ coincide, and the integral $\int _{X}u(x,s(x))d\mu -\int _{Y}v(y,t(y))d\nu $ is maximal. We give condition on $u$ and $v$ for which there is a unique solution.
LA - eng
KW - optimal transportation; measure-preserving maps
UR - http://eudml.org/doc/246109
ER -