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

TL;DR

This paper extends Liouville-type theorems for fully nonlinear elliptic equations in half spaces by removing boundedness assumptions on solutions and establishing results for supersolutions involving Pucci extremal operators.

Contribution

It removes the boundedness requirement in Liouville-type theorems for fully nonlinear elliptic equations and systems in half spaces, broadening their applicability.

Findings

Liouville-type theorems hold without boundedness assumptions.

Results for supersolutions with Pucci extremal operators.

Decay estimates for solutions in half spaces.

Abstract

In \cite{LWZ}, 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 \cite{LWZ} 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.