Liouville-type theorems for fully nonlinear elliptic equation in half spaces

2012/09/05 by Guozhen Lu, Lu, Guozhen, Jiuyi Zhu +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1209.1144

Some typos are corrected and a few references are added

arxiv created 2012/09/09 · arxiv updated 2012/09/11

Abstract

In \citeLWZ, we establish Liouville-type theorems and decay estimates for solutions of a class of high order elliptic equations and systems without the boundedness assumptions on the solutions. In this paper, we continue our work in \citeLWZ to investigate the role of boundedness assumption in proving Liouville-type theorems for fully nonlinear equations. We remove the boundedness assumption of solutions which was required in the proof of Liouville-type theorems for fully nonlinear elliptic equations or systems in half spaces. We also prove the Liouville-type theorems for supersolutions of a system of fully nonlinear equations with Pucci extremal operators in half spaces.

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• Liouville theorems for fully nonlinear elliptic equations on half spaces
• Explicit subsolutions and a Liouville theorem for fully nonlinear uniformly elliptic inequalities in halfspaces
• Liouville properties and critical value of fully nonlinear elliptic\n operators
• Liouville theorems on the upper half space
• Liouville type theorems for stable solutions of certain elliptic systems