Continuity of an optimal transport in Monge problem
Fragala I, Gelli MS, Pratelli A (2005)
Publication Language: English
Publication Status: Published
Publication Type: Journal article
Publication year: 2005
Journal
Publisher: Elsevier
Book Volume: 84
Pages Range: 1261-1294
Journal Issue: 9
DOI: 10.1016/j.matpur.2005.02.002
Abstract
Given two absolutely continuous probability measures f(+/-) in R-2, we consider the classical Monge transport problem, with the Euclidean distance as cost function. We prove the existence of a continuous optimal transport, under the assumptions that (the densities of) f(+/-) are continuous and strictly AA positive in the interior part of their supports, and that such supports are convex, compact, and disjoint. We show through several examples that our statement is nearly optimal. Moreover, under the same hypotheses, we also obtain the continuity of the transport density. (c) 2005 Elsevier SAS. All rights reserved.
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APA:
Fragala, I., Gelli, M.S., & Pratelli, A. (2005). Continuity of an optimal transport in Monge problem. Journal De Mathematiques Pures Et Appliquees, 84(9), 1261-1294. https://doi.org/10.1016/j.matpur.2005.02.002
MLA:
Fragala, Ilaria, Maria Stella Gelli, and Aldo Pratelli. "Continuity of an optimal transport in Monge problem." Journal De Mathematiques Pures Et Appliquees 84.9 (2005): 1261-1294.
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