A note on the classification of positive solutions to the critical p-Laplace equation in $\mathbb{R}^n$

TL;DR

This paper classifies positive solutions to the critical p-Laplace equation in high-dimensional Euclidean space, refining previous results by relaxing the conditions on the parameter p.

Contribution

It provides a new classification result for positive solutions of the critical p-Laplace equation, extending the range of p for which solutions are characterized.

Findings

Classification of solutions for p > p_n in R^n

Improves upon previous results by Ou

Extends the range of p for solution classification

Abstract

In this note, we obtain a classification result for positive solutions to the critical p-Laplace equation in $\mathbb{R}^n$ with $n\ge4$ and $p>p_n$ for some number $p_n\in\left(\frac{n}{3},\frac{n+1}{3}\right)$ such that $p_n\sim\frac{n}{3}+\frac{1}{n}$, which slightly improves upon a similar result recently obtained by Ou under the condition $p\ge\frac{n+1}{3}$.