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On Hölder continuity-in-time of the optimal transport map towards measures along a curve

Published online by Cambridge University Press:  31 March 2011

Nicola Gigli
Affiliation:
UFR Mathématiques et Informatique, Université de Bordeaux, 351 cours de la Libération, 33405 Talence cedex, France
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Abstract

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We discuss the problem of the regularity-in-time of the map tTtLp(ℝd, ℝd; σ), where Tt is a transport map (optimal or not) from a reference measure σ to a measure μt which lies along an absolutely continuous curve tμt in the space (). We prove that in most cases such a map is no more than 1/p-Hölder continuous.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2011

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