Regularity of potential functions of the optimal transportation problem

Xi Nan Ma; Neil S. Trudinger; Xu Jia Wang

doi:10.1007/s00205-005-0362-9

Regularity of potential functions of the optimal transportation problem

Xi Nan Ma^*, Neil S. Trudinger, Xu Jia Wang

^*Corresponding author for this work

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

254 Citations (Scopus)

Abstract

The potential function of the optimal transportation problem satisfies a partial differential equation of Monge-Ampère type. In this paper we introduce the notion of a generalized solution, and prove the existence and uniqueness of generalized solutions of the problem. We also prove the solution is smooth under certain structural conditions on the cost function.

Original language	English
Pages (from-to)	151-183
Number of pages	33
Journal	Archive for Rational Mechanics and Analysis
Volume	177
Issue number	2
DOIs	https://doi.org/10.1007/s00205-005-0362-9
Publication status	Published - Aug 2005

Access to Document

10.1007/s00205-005-0362-9

Cite this

@article{017351af01c64c338252fa994b7cbf3a,

title = "Regularity of potential functions of the optimal transportation problem",

abstract = "The potential function of the optimal transportation problem satisfies a partial differential equation of Monge-Amp{\`e}re type. In this paper we introduce the notion of a generalized solution, and prove the existence and uniqueness of generalized solutions of the problem. We also prove the solution is smooth under certain structural conditions on the cost function.",

author = "Ma, {Xi Nan} and Trudinger, {Neil S.} and Wang, {Xu Jia}",

year = "2005",

month = aug,

doi = "10.1007/s00205-005-0362-9",

language = "English",

volume = "177",

pages = "151--183",

journal = "Archive for Rational Mechanics and Analysis",

issn = "0003-9527",

publisher = "Springer",

number = "2",

}

TY - JOUR

T1 - Regularity of potential functions of the optimal transportation problem

AU - Ma, Xi Nan

AU - Trudinger, Neil S.

AU - Wang, Xu Jia

PY - 2005/8

Y1 - 2005/8

N2 - The potential function of the optimal transportation problem satisfies a partial differential equation of Monge-Ampère type. In this paper we introduce the notion of a generalized solution, and prove the existence and uniqueness of generalized solutions of the problem. We also prove the solution is smooth under certain structural conditions on the cost function.

AB - The potential function of the optimal transportation problem satisfies a partial differential equation of Monge-Ampère type. In this paper we introduce the notion of a generalized solution, and prove the existence and uniqueness of generalized solutions of the problem. We also prove the solution is smooth under certain structural conditions on the cost function.

UR - http://www.scopus.com/inward/record.url?scp=22944479926&partnerID=8YFLogxK

U2 - 10.1007/s00205-005-0362-9

DO - 10.1007/s00205-005-0362-9

M3 - Article

SN - 0003-9527

VL - 177

SP - 151

EP - 183

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 2

ER -

Regularity of potential functions of the optimal transportation problem

Abstract

Access to Document

Other files and links

Fingerprint

Cite this