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

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