On the Dirichlet problem for general augmented Hessian equations

Feida Jiang; Neil S. Trudinger

doi:10.1016/j.jde.2020.04.004

On the Dirichlet problem for general augmented Hessian equations

Feida Jiang, Neil S. Trudinger^*

^*Corresponding author for this work

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

19 Citations (Scopus)

Abstract

In this paper we apply various first and second derivative estimates and barrier constructions from our treatment of oblique boundary value problems for augmented Hessian equations, to the case of Dirichlet boundary conditions. As a result we extend our previous results on the Monge-Ampère and k-Hessian cases to general classes of augmented Hessian equations in Euclidean space.

Original language	English
Pages (from-to)	5204-5227
Number of pages	24
Journal	Journal of Differential Equations
Volume	269
Issue number	6
DOIs	https://doi.org/10.1016/j.jde.2020.04.004
Publication status	Published - 5 Sept 2020

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10.1016/j.jde.2020.04.004

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title = "On the Dirichlet problem for general augmented Hessian equations",

abstract = "In this paper we apply various first and second derivative estimates and barrier constructions from our treatment of oblique boundary value problems for augmented Hessian equations, to the case of Dirichlet boundary conditions. As a result we extend our previous results on the Monge-Amp{\`e}re and k-Hessian cases to general classes of augmented Hessian equations in Euclidean space.",

keywords = "Augmented Hessian equations, Dirichlet problem, Regular matrix, Second derivative estimates",

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

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2020",

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doi = "10.1016/j.jde.2020.04.004",

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T1 - On the Dirichlet problem for general augmented Hessian equations

AU - Jiang, Feida

AU - Trudinger, Neil S.

PY - 2020/9/5

Y1 - 2020/9/5

N2 - In this paper we apply various first and second derivative estimates and barrier constructions from our treatment of oblique boundary value problems for augmented Hessian equations, to the case of Dirichlet boundary conditions. As a result we extend our previous results on the Monge-Ampère and k-Hessian cases to general classes of augmented Hessian equations in Euclidean space.

AB - In this paper we apply various first and second derivative estimates and barrier constructions from our treatment of oblique boundary value problems for augmented Hessian equations, to the case of Dirichlet boundary conditions. As a result we extend our previous results on the Monge-Ampère and k-Hessian cases to general classes of augmented Hessian equations in Euclidean space.

KW - Augmented Hessian equations

KW - Dirichlet problem

KW - Regular matrix

KW - Second derivative estimates

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U2 - 10.1016/j.jde.2020.04.004

DO - 10.1016/j.jde.2020.04.004

M3 - Article

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VL - 269

SP - 5204

EP - 5227

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 6

ER -

On the Dirichlet problem for general augmented Hessian equations

Abstract

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