We prove the existence of an optimal transport map for the Monge problem in a convex bounded subset of Rd under the assumptions that the first marginal is absolutely continuous with respect to the Lebesgue measure and that the cost is given by a strictly convex norm. We propose a new approach which does not use disintegration of measures.
|Autori:||CHAMPION T; DE PASCALE L|
|Titolo:||The Monge problem for strictly convex norms in R^N|
|Anno del prodotto:||2010|
|Digital Object Identifier (DOI):||10.4171/JEMS/234|
|Appare nelle tipologie:||1.1 Articolo in rivista|