A strategy for non-strictly convex transport costs and the example of ||x-y||p in \mathbb R2 - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Communications in Mathematical Sciences Année : 2010

A strategy for non-strictly convex transport costs and the example of ||x-y||p in \mathbb R2

Résumé

This paper deals with the existence of optimal transport maps for some optimal transport problems with a convex but non strictly convex cost. We give a decomposition strategy to address this issue. As part of our strategy, we have to treat some transport problems, of independent interest, with a convex constraint on the displacement. As an illustration of our strategy, we prove existence of optimal transport maps in the case where the source measure is absolutely continuous with respect to the Lebesgue measure and the transportation cost is of the form h(||x-y||) with h strictly convex increasing and ||. || an arbitrary norm in \R2.
Fichier principal
Vignette du fichier
mongeconstrPREP.pdf (160.13 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00417303 , version 1 (15-09-2009)

Identifiants

Citer

Guillaume Carlier, Luigi de Pascale, Filippo Santambrogio. A strategy for non-strictly convex transport costs and the example of ||x-y||p in \mathbb R2. Communications in Mathematical Sciences, 2010, à paraître. ⟨hal-00417303⟩
131 Consultations
115 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More