Gradient estimates for solutions to quasilinear elliptic equations with critical sobolev growth and hardy potential

This note is a continuation of the work 17]. We study the following quasilinear elliptic equations $-{\Delta }_{p}u-\frac{\mu }{{\left|x\right|}^p}{\left|u\right|}^{p-2}u=Q\left(x\right)\left|u\right|\frac{N_p}{N-p}-2u,x\in {?}^N,$ where 1 < p < N,0 ≤ μ < ((N-p)/p)^p and Q ? L^∞ ?^N. Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.