Transport problems and disintegration maps

Luca Granieri; Francesco Maddalena

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

  • Volume: 19, Issue: 3, page 888-905
  • ISSN: 1292-8119

Abstract

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By disintegration of transport plans it is introduced the notion of transport class. This allows to consider the Monge problem as a particular case of the Kantorovich transport problem, once a transport class is fixed. The transport problem constrained to a fixed transport class is equivalent to an abstract Monge problem over a Wasserstein space of probability measures. Concerning solvability of this kind of constrained problems, it turns out that in some sense the Monge problem corresponds to a lucky case.

How to cite

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Granieri, Luca, and Maddalena, Francesco. "Transport problems and disintegration maps." ESAIM: Control, Optimisation and Calculus of Variations 19.3 (2013): 888-905. <http://eudml.org/doc/272859>.

@article{Granieri2013,
abstract = {By disintegration of transport plans it is introduced the notion of transport class. This allows to consider the Monge problem as a particular case of the Kantorovich transport problem, once a transport class is fixed. The transport problem constrained to a fixed transport class is equivalent to an abstract Monge problem over a Wasserstein space of probability measures. Concerning solvability of this kind of constrained problems, it turns out that in some sense the Monge problem corresponds to a lucky case.},
author = {Granieri, Luca, Maddalena, Francesco},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {optimal mass transportation theory; Monge − Kantorovich problem; calculus of variations; shape analysis; geometric measure theory; Monge-Kantorovich problem},
language = {eng},
number = {3},
pages = {888-905},
publisher = {EDP-Sciences},
title = {Transport problems and disintegration maps},
url = {http://eudml.org/doc/272859},
volume = {19},
year = {2013},
}

TY - JOUR
AU - Granieri, Luca
AU - Maddalena, Francesco
TI - Transport problems and disintegration maps
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2013
PB - EDP-Sciences
VL - 19
IS - 3
SP - 888
EP - 905
AB - By disintegration of transport plans it is introduced the notion of transport class. This allows to consider the Monge problem as a particular case of the Kantorovich transport problem, once a transport class is fixed. The transport problem constrained to a fixed transport class is equivalent to an abstract Monge problem over a Wasserstein space of probability measures. Concerning solvability of this kind of constrained problems, it turns out that in some sense the Monge problem corresponds to a lucky case.
LA - eng
KW - optimal mass transportation theory; Monge − Kantorovich problem; calculus of variations; shape analysis; geometric measure theory; Monge-Kantorovich problem
UR - http://eudml.org/doc/272859
ER -

References

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