Please use this identifier to cite or link to this item:
Title: A Proof of Monge Problem in R^n by Stability
Authors: Caravenna, Laura
Keywords: Monge ProblemArea EstimatesDisintegration of Measures
Issue Date: 2011
Publisher: EUT Edizioni Università di Trieste
Source: Laura Caravenna, "A Proof of Monge Problem in R^n by Stability", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 43 (2011), pp. 31–51
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
43 (2011)
The Monge problem in R^n, with a possibly asymmetric norm cost function and absolutely continuous first marginal, is generally underdetermined. An optimal transport plan is selected by a secondary variational problem, from a work on crystalline norms. In this way the mass still moves along lines. The paper provides a quantitative absolute continuity push forward estimate for the translation along
these lines: the consequent area formula, for the disintegration of the
Lebesgue measure w.r.t. the partition into these 1D-rays, shows that
the conditional measures are absolutely continuous, and yields uniqueness of the optimal secondary transport plan non-decreasing along rays,
recovering that it is induced by a map.
Type: Article
ISSN: 0049-4704
eISSN: 2464-8728
Appears in Collections:Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.43 (2011)

Files in This Item:
File Description SizeFormat
CaravennaRendMat43.pdf711.42 kBAdobe PDFThumbnail
Show full item record

CORE Recommender

Page view(s) 50

checked on Aug 4, 2021

Download(s) 50

checked on Aug 4, 2021

Google ScholarTM


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.