# 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

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topGranieri, 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 -

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