A note on the Liouville theorem of fully nonlinear elliptic equations

TL;DR

This paper introduces a novel approach to analyze the asymptotic behavior of solutions to fully nonlinear elliptic equations in exterior domains, independent of regularity and dimension constraints.

Contribution

The paper presents a new method for studying the Liouville theorem for fully nonlinear elliptic equations that does not rely on the regularity of the operator or the dimension.

Findings

New method for asymptotic analysis of solutions

Applicable without $C^2$ regularity assumptions

Independent of the dimension $n$

Abstract

In this paper, a new method is presented to investigate the asymptotic behavior of solutions to the fully nonlinear uniformly elliptic equation $F(D^2u)=0$ in exterior domains. This method does not depend on the $C^2$ regularity of $F$ and the dimension $n$.