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15 April 2011 The Monge problem in Rd
Thierry Champion, Luigi De Pascale
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Duke Math. J. 157(3): 551-572 (15 April 2011). DOI: 10.1215/00127094-1272939

Abstract

We first consider the Monge problem in a convex bounded subset of Rd. The cost is given by a general norm, and we prove the existence of an optimal transport map under the classical assumption that the first marginal is absolutely continuous with respect to the Lebesgue measure. In the final part of the paper we show how to extend this existence result to a general open subset of Rd.

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Thierry Champion. Luigi De Pascale. "The Monge problem in Rd." Duke Math. J. 157 (3) 551 - 572, 15 April 2011. https://doi.org/10.1215/00127094-1272939

Information

Published: 15 April 2011
First available in Project Euclid: 1 April 2011

zbMATH: 1232.49050
MathSciNet: MR2785830
Digital Object Identifier: 10.1215/00127094-1272939

Subjects:
Primary: 49J45
Secondary: 49K30 , 49Q20

Rights: Copyright © 2011 Duke University Press

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Vol.157 • No. 3 • 15 April 2011
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