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arXiv · 1207.4026

Transport Problems and Disintegration Maps

L. Granieri·F. Maddalena
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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.

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L. Granieri, F. Maddalena. 2012-07-17. Transport Problems and Disintegration Maps. https://arxiv.org/abs/1207.4026

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