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Transport problems and disintegration maps

Published online by Cambridge University Press:  03 June 2013

Luca Granieri  and
Francesco Maddalena
Luca Granieri
Affiliation:
Dipartimento di Matematica Politecnico di Bari, via Orabona 4, 70125 Bari, Italy. l.granieri@poliba.it; f.maddalena@poliba.it
Francesco Maddalena
Affiliation:
Dipartimento di Matematica Politecnico di Bari, via Orabona 4, 70125 Bari, Italy. l.granieri@poliba.it; f.maddalena@poliba.it
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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.

Keywords

Optimal mass transportation theoryMonge − Kantorovich problemcalculus of variationsshape analysisgeometric measure theory
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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