A new proof for the regularity of Monge-AmpÈre type equations

Xu Jia Wang; Yating Wu

doi:10.4310/JDG/1606964417

A new proof for the regularity of Monge-AmpÈre type equations

Xu Jia Wang^*, Yating Wu

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

By employing the Green function, in this paper we provide a new and elementary proof for the interior regularity of solutions to the Monge-Ampère equation. This proof also applies to the complex Monge-Ampère equation and the k-Hessian equation.

Original language	English
Pages (from-to)	543-553
Number of pages	11
Journal	Journal of Differential Geometry
Volume	116
Issue number	3
DOIs	https://doi.org/10.4310/JDG/1606964417
Publication status	Published - 2020

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title = "A new proof for the regularity of Monge-Amp{\`E}re type equations",

abstract = "By employing the Green function, in this paper we provide a new and elementary proof for the interior regularity of solutions to the Monge-Amp{\`e}re equation. This proof also applies to the complex Monge-Amp{\`e}re equation and the k-Hessian equation.",

keywords = "Monge-Amp{\`e}re equation, Regularity",

author = "Wang, \{Xu Jia\} and Yating Wu",

year = "2020",

doi = "10.4310/JDG/1606964417",

language = "English",

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journal = "Journal of Differential Geometry",

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T1 - A new proof for the regularity of Monge-AmpÈre type equations

AU - Wang, Xu Jia

AU - Wu, Yating

PY - 2020

Y1 - 2020

N2 - By employing the Green function, in this paper we provide a new and elementary proof for the interior regularity of solutions to the Monge-Ampère equation. This proof also applies to the complex Monge-Ampère equation and the k-Hessian equation.

AB - By employing the Green function, in this paper we provide a new and elementary proof for the interior regularity of solutions to the Monge-Ampère equation. This proof also applies to the complex Monge-Ampère equation and the k-Hessian equation.

KW - Monge-Ampère equation

KW - Regularity

UR - https://www.scopus.com/pages/publications/85098141956

U2 - 10.4310/JDG/1606964417

DO - 10.4310/JDG/1606964417

M3 - Article

SN - 0022-040X

VL - 116

SP - 543

EP - 553

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

IS - 3

ER -

A new proof for the regularity of Monge-AmpÈre type equations

Abstract

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