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^*

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Normal University

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

4 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1561-1578
Number of pages	18
Journal	Discrete and Continuous Dynamical Systems
Volume	41
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2020331
Publication status	Published - Apr 2021

Keywords

A priori estimate
Half-space
Liouville theorem
Parabolic monge-ampère equations

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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.",

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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.

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KW - Half-space

KW - Liouville theorem

KW - Parabolic monge-ampère equations

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

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Keywords

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