A liouville theorem of parabolic monge-ampère equations in half-space

Ziwei Zhou; Jiguang Bao; Bo Wang

doi:10.3934/dcds.2020331

A liouville theorem of parabolic monge-ampère equations in half-space

Ziwei Zhou
, Jiguang Bao
, Bo Wang^*

^*此作品的通讯作者

数学学院

Beijing Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

7 引用（Scopus）

摘要

In this paper, we establish the gradient and second derivative estimates for solutions to two kinds of parabolic Monge-Ampère equations in half-space under certain boundary data and growth condition. We also use such estimates to obtain the Liouville theorems for these two kinds of parabolic Monge-Ampère equations and one kind of elliptic Monge-Ampère equation.

源语言	英语
页（从-至）	1561-1578
页数	18
期刊	Discrete and Continuous Dynamical Systems
卷	41
期	4
DOI	https://doi.org/10.3934/dcds.2020331
出版状态	已出版 - 4月 2021

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title = "A liouville theorem of parabolic monge-amp{\`e}re equations in half-space",

abstract = "In this paper, we establish the gradient and second derivative estimates for solutions to two kinds of parabolic Monge-Amp{\`e}re equations in half-space under certain boundary data and growth condition. We also use such estimates to obtain the Liouville theorems for these two kinds of parabolic Monge-Amp{\`e}re equations and one kind of elliptic Monge-Amp{\`e}re equation.",

keywords = "A priori estimate, Half-space, Liouville theorem, Parabolic monge-amp{\`e}re equations",

author = "Ziwei Zhou and Jiguang Bao and Bo Wang",

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AU - Bao, Jiguang

AU - Wang, Bo

PY - 2021/4

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N2 - In this paper, we establish the gradient and second derivative estimates for solutions to two kinds of parabolic Monge-Ampère equations in half-space under certain boundary data and growth condition. We also use such estimates to obtain the Liouville theorems for these two kinds of parabolic Monge-Ampère equations and one kind of elliptic Monge-Ampère equation.

AB - In this paper, we establish the gradient and second derivative estimates for solutions to two kinds of parabolic Monge-Ampère equations in half-space under certain boundary data and growth condition. We also use such estimates to obtain the Liouville theorems for these two kinds of parabolic Monge-Ampère equations and one kind of elliptic Monge-Ampère equation.

KW - A priori estimate

KW - Half-space

KW - Liouville theorem

KW - Parabolic monge-ampère equations

UR - https://www.scopus.com/pages/publications/85101332691

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DO - 10.3934/dcds.2020331

M3 - Article

AN - SCOPUS:85101332691

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JO - Discrete and Continuous Dynamical Systems

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ER -

A liouville theorem of parabolic monge-ampère equations in half-space

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