In some recent papers it is proved that, under natural assumptions on the first marginal, the Monge problem in the metric space Rd equipped with a general norm admits a solution. Although the basic idea of the solution is simple the proof involves some very complex technical results. Here we will report a proof of the result in the simpler case of uniformly convex norms. Uniform convexity allow us to reduce the technical burdens while still giving the main ideas of the general proof. The proof of the density of the transport set given in this paper is original.

The Monge problem in R^d: variations on a theme II

DE PASCALE, LUIGI
2011-01-01

Abstract

In some recent papers it is proved that, under natural assumptions on the first marginal, the Monge problem in the metric space Rd equipped with a general norm admits a solution. Although the basic idea of the solution is simple the proof involves some very complex technical results. Here we will report a proof of the result in the simpler case of uniformly convex norms. Uniform convexity allow us to reduce the technical burdens while still giving the main ideas of the general proof. The proof of the density of the transport set given in this paper is original.
2011
DE PASCALE, Luigi
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/586079
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? ND
social impact