A Liouville theorem of degenerate elliptic equation and its application

TL;DR

This paper proves a Liouville theorem for certain degenerate elliptic equations using the moving plane method and applies it to establish bounds for positive solutions of related semi-linear equations.

Contribution

It introduces a Liouville theorem for degenerate elliptic equations and demonstrates its application in deriving a priori bounds for solutions.

Findings

Liouville theorem for degenerate elliptic equations established

A priori bounds for positive solutions derived

Application of moving plane method to degenerate equations

Abstract

In this paper, we apply the moving plane method to some degenerate elliptic equations to get a Liouville type theorem. As an application, we derive the a priori bounds for positive solutions of some semi-linear degenerate elliptic equations.