On the Dirichlet problem for Monge-Ampère type equations

Feida Jiang; Neil S. Trudinger; Xiao Ping Yang

doi:10.1007/s00526-013-0619-3

On the Dirichlet problem for Monge-Ampère type equations

Feida Jiang, Neil S. Trudinger, Xiao Ping Yang

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

43 Citations (Scopus)

Abstract

In this paper, we prove second derivative estimates together with classical solvability for the Dirichlet problem of certain Monge-Ampére type equations under sharp hypotheses. In particular we assume that the matrix function in the augmented Hessian is regular in the sense used by Trudinger and Wang in Ann. Scoula Norm. Sup. Pisa Cl. Sci. VIII, 143-174 2009 in their study of global regularity in optimal transportation as well as the existence of a smooth subsolution. The latter hypothesis replaces a barrier condition also used in their work. The applications to optimal transportation and prescribed Jacobian equations are also indicated.

Original language	English
Pages (from-to)	1223-1236
Number of pages	14
Journal	Calculus of Variations and Partial Differential Equations
Volume	49
Issue number	3-4
DOIs	https://doi.org/10.1007/s00526-013-0619-3
Publication status	Published - Mar 2014

Access to Document

10.1007/s00526-013-0619-3

Cite this

@article{d11b426f028445cda737ef9867339319,

title = "On the Dirichlet problem for Monge-Amp{\`e}re type equations",

abstract = "In this paper, we prove second derivative estimates together with classical solvability for the Dirichlet problem of certain Monge-Amp{\'e}re type equations under sharp hypotheses. In particular we assume that the matrix function in the augmented Hessian is regular in the sense used by Trudinger and Wang in Ann. Scoula Norm. Sup. Pisa Cl. Sci. VIII, 143-174 2009 in their study of global regularity in optimal transportation as well as the existence of a smooth subsolution. The latter hypothesis replaces a barrier condition also used in their work. The applications to optimal transportation and prescribed Jacobian equations are also indicated.",

author = "Feida Jiang and Trudinger, {Neil S.} and Yang, {Xiao Ping}",

year = "2014",

month = mar,

doi = "10.1007/s00526-013-0619-3",

language = "English",

volume = "49",

pages = "1223--1236",

journal = "Calculus of Variations and Partial Differential Equations",

issn = "0944-2669",

publisher = "Springer",

number = "3-4",

}

TY - JOUR

T1 - On the Dirichlet problem for Monge-Ampère type equations

AU - Jiang, Feida

AU - Trudinger, Neil S.

AU - Yang, Xiao Ping

PY - 2014/3

Y1 - 2014/3

N2 - In this paper, we prove second derivative estimates together with classical solvability for the Dirichlet problem of certain Monge-Ampére type equations under sharp hypotheses. In particular we assume that the matrix function in the augmented Hessian is regular in the sense used by Trudinger and Wang in Ann. Scoula Norm. Sup. Pisa Cl. Sci. VIII, 143-174 2009 in their study of global regularity in optimal transportation as well as the existence of a smooth subsolution. The latter hypothesis replaces a barrier condition also used in their work. The applications to optimal transportation and prescribed Jacobian equations are also indicated.

AB - In this paper, we prove second derivative estimates together with classical solvability for the Dirichlet problem of certain Monge-Ampére type equations under sharp hypotheses. In particular we assume that the matrix function in the augmented Hessian is regular in the sense used by Trudinger and Wang in Ann. Scoula Norm. Sup. Pisa Cl. Sci. VIII, 143-174 2009 in their study of global regularity in optimal transportation as well as the existence of a smooth subsolution. The latter hypothesis replaces a barrier condition also used in their work. The applications to optimal transportation and prescribed Jacobian equations are also indicated.

UR - http://www.scopus.com/inward/record.url?scp=84894583622&partnerID=8YFLogxK

U2 - 10.1007/s00526-013-0619-3

DO - 10.1007/s00526-013-0619-3

M3 - Article

SN - 0944-2669

VL - 49

SP - 1223

EP - 1236

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 3-4

ER -

On the Dirichlet problem for Monge-Ampère type equations

Abstract

Access to Document

Other files and links

Fingerprint

Cite this