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Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/5716

Title: A Proof of Monge Problem in R^n by Stability
Authors: Caravenna, Laura
Keywords: Monge Problem
Area Estimates
Disintegration of Measures
Issue Date: 2011
Publisher: EUT Edizioni Università di Trieste
Citation: 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)
Abstract: 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.
URI: http://hdl.handle.net/10077/5716
ISSN: 0049-4704
MS Classification 2000: 49J45
49K30
28A50
49Q20
Appears in Collections:Rendiconti dell' Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.43 (2011)

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