Open Access
2016 Boundary $C^{1,\alpha}$ regularity of potential functions in optimal transportation with quadratic cost
Elina Andriyanova, Shibing Chen
Anal. PDE 9(6): 1483-1496 (2016). DOI: 10.2140/apde.2016.9.1483

Abstract

We provide a different proof for the global C1,α regularity of potential functions in the optimal transport problem, which was originally proved by Caffarelli. Our method applies to a more general class of domains.

Citation

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Elina Andriyanova. Shibing Chen. "Boundary $C^{1,\alpha}$ regularity of potential functions in optimal transportation with quadratic cost." Anal. PDE 9 (6) 1483 - 1496, 2016. https://doi.org/10.2140/apde.2016.9.1483

Information

Received: 20 November 2015; Revised: 8 March 2016; Accepted: 29 April 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1350.35049
MathSciNet: MR3555318
Digital Object Identifier: 10.2140/apde.2016.9.1483

Subjects:
Primary: 35B45 , 35J60 , 35J96 , 49Q20

Keywords: boundary regularity , Optimal transport , quadratic cost

Rights: Copyright © 2016 Mathematical Sciences Publishers

Vol.9 • No. 6 • 2016
MSP
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