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.
|Autori interni:||MADDALENA, Francesco|
|Titolo:||Transport Problems and Disintegration Maps|
|Rivista:||ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS|
|Data di pubblicazione:||2012|
|Digital Object Identifier (DOI):||10.1051/cocv/2012037|
|Appare nelle tipologie:||1.1 Articolo in rivista|