Gradient Estimates for Solutions To Quasilinear Elliptic Equations with Critical Sobolev Growth and Hardy Potential

This note is a continuation of the work \cite{CaoXiangYan2014}. We study the following quasilinear elliptic equations $-Δ_{p}u-\fracμ{|x|^{p}}|u|^{p-2}u=Q(x)|u|^{\frac{Np}{N-p}-2}u,\quad\, x\in\mathbb{R}^{N},$ where $1<p<N,0\leqμ<\left((N-p)/p\right)^{p}$ and $Q\in L^{\infty}(\R^{N})$. Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.

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