Isolated singularities of solutions of certain quasi-linear elliptic inequalities

TL;DR

This paper classifies the asymptotic behavior of solutions near isolated singularities for a class of quasi-linear elliptic inequalities, extending understanding of solution behavior in nonlinear PDEs.

Contribution

It provides a complete classification of the asymptotic behavior of solutions with isolated singularities for a specific class of quasi-linear elliptic inequalities.

Findings

Complete classification of asymptotic behaviors.

Identification of conditions for singularity types.

Extension of known results to broader inequality class.

Abstract

We provide a complete classification of the asymptotic behavior of isolated singularities for solutions satisfying \[ 0\le-\Delta_{p}u(x)\le \tau u^{\frac{n(p-1)}{n-p}} (x),\,\,u(x)\ge0,\,\,1<p<n,\,\,n\ge2, \]where $u(x)\in C^2(B(0,1)\backslash\{0\})$ and $B(0,1)\subset \mathbb R^n$.