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Transport problems and disintegration maps
Published online by Cambridge University Press: 03 June 2013
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.
Keywords
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- Type
- Research Article
- Information
- ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 3 , July 2013, pp. 888 - 905
- Copyright
- © EDP Sciences, SMAI, 2013
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