A Liouville theorem of parabolic Monge-AmpÈre equations in half-space

Ziwei Zhou; Jiguang Bao; Bo Wang

doi:10.3934/dcds.2020331

Article Contents

2021, Volume 41, Issue 4: 1561-1578. Doi: 10.3934/dcds.2020331

This issue Previous Article Jordan decomposition and the recurrent set of flows of automorphisms Next Article Well-posedness for the three dimensional stochastic planetary geostrophic equations of large-scale ocean circulation

A Liouville theorem of parabolic Monge-AmpÈre equations in half-space

1.
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China
2.
School of Mathematics and Statistics, Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 100081, China

^* Corresponding author: Bo Wang
^* Corresponding author: Bo Wang

Received: January 31, 2020

Revised: May 31, 2020

Early access: September 2020

Published: April 2021

The first and second author are partially supported by NSFC 11871102 and 11631002. The third author is partially supported by NSFC 11701027 and Beijing Institute of Technology Research Fund Program for Young Scholars

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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.

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Mathematics Subject Classification: 35K96, 35B53.

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