Interior C2,α regularity for potential functions in optimal transportation

Jiakun Liu; Neil S. Trudinger; Xu Jia Wang

doi:10.1080/03605300903236609

Interior C^2,α regularity for potential functions in optimal transportation

Jiakun Liu
, Neil S. Trudinger
, Xu Jia Wang

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

48 Citations (Scopus)

Abstract

In this paper we study the continuity of second derivatives of solutions to the Monge-Ampère equation arising in optimal transportation. We obtain Hölder and more general continuity estimates for second derivatives, when the inhomogeneous term is Hölder and Dini continuous, together with corresponding regularity results for potentials.

Original language	English
Pages (from-to)	165-184
Number of pages	20
Journal	Communications in Partial Differential Equations
Volume	35
Issue number	1
DOIs	https://doi.org/10.1080/03605300903236609
Publication status	Published - 2009

Access to Document

10.1080/03605300903236609

Cite this

@article{41c35faf1f0f4e329de7477b09977de7,

title = "Interior C2,α regularity for potential functions in optimal transportation",

abstract = "In this paper we study the continuity of second derivatives of solutions to the Monge-Amp{\`e}re equation arising in optimal transportation. We obtain H{\"o}lder and more general continuity estimates for second derivatives, when the inhomogeneous term is H{\"o}lder and Dini continuous, together with corresponding regularity results for potentials.",

keywords = "Monge-Amp{\`e}re equations, Optimal transportation, Second derivative estimates",

author = "Jiakun Liu and Trudinger, \{Neil S.\} and Wang, \{Xu Jia\}",

year = "2009",

doi = "10.1080/03605300903236609",

language = "English",

volume = "35",

pages = "165--184",

journal = "Communications in Partial Differential Equations",

issn = "0360-5302",

publisher = "Taylor and Francis Ltd.",

number = "1",

}

TY - JOUR

T1 - Interior C2,α regularity for potential functions in optimal transportation

AU - Liu, Jiakun

AU - Trudinger, Neil S.

AU - Wang, Xu Jia

PY - 2009

Y1 - 2009

N2 - In this paper we study the continuity of second derivatives of solutions to the Monge-Ampère equation arising in optimal transportation. We obtain Hölder and more general continuity estimates for second derivatives, when the inhomogeneous term is Hölder and Dini continuous, together with corresponding regularity results for potentials.

AB - In this paper we study the continuity of second derivatives of solutions to the Monge-Ampère equation arising in optimal transportation. We obtain Hölder and more general continuity estimates for second derivatives, when the inhomogeneous term is Hölder and Dini continuous, together with corresponding regularity results for potentials.

KW - Monge-Ampère equations

KW - Optimal transportation

KW - Second derivative estimates

UR - https://www.scopus.com/pages/publications/74949099148

U2 - 10.1080/03605300903236609

DO - 10.1080/03605300903236609

M3 - Article

SN - 0360-5302

VL - 35

SP - 165

EP - 184

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 1

ER -

Interior C^2,α regularity for potential functions in optimal transportation

Abstract

Access to Document

Other files and links

Fingerprint

Cite this