| Issue |
ESAIM: COCV
Volume 19, Number 3, July-September 2013
|
|
|---|---|---|
| Page(s) | 888 - 905 | |
| DOI | https://doi.org/10.1051/cocv/2012037 | |
| Published online | 03 June 2013 | |
Transport problems and disintegration maps
Dipartimento di Matematica Politecnico di Bari,
via Orabona 4, 70125
Bari,
Italy
l.granieri@poliba.it; f.maddalena@poliba.it
Received: 6 July 2012
Revised: 26 September 2012
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.
Mathematics Subject Classification: 37J50 / 49Q20 / 49Q15
Key words: Optimal mass transportation theory / Monge − Kantorovich problem / calculus of variations / shape analysis / geometric measure theory
© EDP Sciences, SMAI, 2013
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