# An optimal matching problem

ESAIM: Control, Optimisation and Calculus of Variations (2005)

- Volume: 11, Issue: 1, page 57-71
- ISSN: 1292-8119

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topEkeland, Ivar. "An optimal matching problem." ESAIM: Control, Optimisation and Calculus of Variations 11.1 (2005): 57-71. <http://eudml.org/doc/246109>.

@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 -

## References

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