Liouville theorems for fully nonlinear elliptic equations on half spaces

TL;DR

This paper establishes two Liouville theorems for fully nonlinear elliptic equations on half spaces, utilizing boundary regularity and estimate techniques, offering a concise new proof approach.

Contribution

It provides novel Liouville theorems for nonlinear elliptic equations on half spaces with a simplified proof method.

Findings

Proved two Liouville theorems for nonlinear elliptic equations.

Developed a shorter proof using boundary regularity and estimates.

Enhanced understanding of solution behavior on half spaces.

Abstract

In this note, we prove two Liouville theorems for fully nonlinear uniformly elliptic equations on half spaces. The main tools are the boundary pointwise regularity, the Hopf type estimate and the Carleson type estimate. Our new proof is rather short.