Isolated singularities of solutions of certain quasi-linear elliptic inequalities

Abstract

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