Hölder regularity of optimal mappings in optimal transportation

Jiakun Liu

doi:10.1007/s00526-008-0190-5

Hölder regularity of optimal mappings in optimal transportation

Jiakun Liu^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

37 Citations (Scopus)

Abstract

It is known that optimal mappings in optimal transportation problems are uniquely determined by corresponding potential functions. In this paper we prove various local properties of potential functions. In particular we obtain the C ^1,α regularity of potential functions with optimal exponent α, which improves previous regularity results of Loeper.

Original language	English
Pages (from-to)	435-451
Number of pages	17
Journal	Calculus of Variations and Partial Differential Equations
Volume	34
Issue number	4
DOIs	https://doi.org/10.1007/s00526-008-0190-5
Publication status	Published - Apr 2009

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title = "H{\"o}lder regularity of optimal mappings in optimal transportation",

abstract = "It is known that optimal mappings in optimal transportation problems are uniquely determined by corresponding potential functions. In this paper we prove various local properties of potential functions. In particular we obtain the C 1,α regularity of potential functions with optimal exponent α, which improves previous regularity results of Loeper.",

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JO - Calculus of Variations and Partial Differential Equations

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Hölder regularity of optimal mappings in optimal transportation

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