On the Dirichlet problem for a class of augmented Hessian equations

Feida Jiang; Neil S. Trudinger; Xiao Ping Yang

doi:10.1016/j.jde.2014.11.005

On the Dirichlet problem for a class of augmented Hessian equations

Feida Jiang^*, Neil S. Trudinger, Xiao Ping Yang

^*Corresponding author for this work

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

27 Citations (Scopus)

Abstract

In this paper, we consider the Dirichlet problem for a new class of augmented Hessian equations. Under sharp assumptions that the matrix function in the augmented Hessian is regular and there exists a smooth subsolution, we establish global second order derivative estimates for the solutions to the Dirichlet problem in bounded domains. The results extend the corresponding results in the previous paper [12] from the Monge-Ampère type equations to the more general Hessian type equations.

Original language	English
Pages (from-to)	1548-1576
Number of pages	29
Journal	Journal of Differential Equations
Volume	258
Issue number	5
DOIs	https://doi.org/10.1016/j.jde.2014.11.005
Publication status	Published - 5 Mar 2015

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title = "On the Dirichlet problem for a class of augmented Hessian equations",

abstract = "In this paper, we consider the Dirichlet problem for a new class of augmented Hessian equations. Under sharp assumptions that the matrix function in the augmented Hessian is regular and there exists a smooth subsolution, we establish global second order derivative estimates for the solutions to the Dirichlet problem in bounded domains. The results extend the corresponding results in the previous paper [12] from the Monge-Amp{\`e}re type equations to the more general Hessian type equations.",

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

note = "Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

year = "2015",

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T1 - On the Dirichlet problem for a class of augmented Hessian equations

AU - Jiang, Feida

AU - Trudinger, Neil S.

AU - Yang, Xiao Ping

PY - 2015/3/5

Y1 - 2015/3/5

N2 - In this paper, we consider the Dirichlet problem for a new class of augmented Hessian equations. Under sharp assumptions that the matrix function in the augmented Hessian is regular and there exists a smooth subsolution, we establish global second order derivative estimates for the solutions to the Dirichlet problem in bounded domains. The results extend the corresponding results in the previous paper [12] from the Monge-Ampère type equations to the more general Hessian type equations.

AB - In this paper, we consider the Dirichlet problem for a new class of augmented Hessian equations. Under sharp assumptions that the matrix function in the augmented Hessian is regular and there exists a smooth subsolution, we establish global second order derivative estimates for the solutions to the Dirichlet problem in bounded domains. The results extend the corresponding results in the previous paper [12] from the Monge-Ampère type equations to the more general Hessian type equations.

UR - https://www.scopus.com/pages/publications/84920644834

U2 - 10.1016/j.jde.2014.11.005

DO - 10.1016/j.jde.2014.11.005

M3 - Article

SN - 0022-0396

VL - 258

SP - 1548

EP - 1576

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 5

ER -

On the Dirichlet problem for a class of augmented Hessian equations

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