We first consider the Monge problem in a convex bounded subset of Rd . The cost is given by a general norm, and we prove the existence of an optimal transport map under the classical assumption that the first marginal is absolutely continuous with respect to the Lebesgue measure. In the final part of the paper we show how to extend this existence result to a general open subset of Rd .
|Autori:||CHAMPION T; DE PASCALE L|
|Titolo:||The Monge Problem in $R^d$|
|Anno del prodotto:||2011|
|Digital Object Identifier (DOI):||10.1215/00127094-1272939|
|Appare nelle tipologie:||1.1 Articolo in rivista|