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

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This note is a continuation of the work CaoXiangYan2014. We study the following quasilinear elliptic equations -Δₚu-μ|x|ᵖ|u|ᵖ⁻²u=Q(x)|u|Np/N-p-2u, xⁿ, 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.