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

Abstract

This note is a continuation of the work [17]. We study the following quasilinear elliptic equations -Δpu-μ|x|p|u|p-2u=Q(x)|u|NpN-p-2u, x∈ℝN, where 1 < p < N,0 ≤ μ < ((N-p)/p)p and Q ɛ L∞ ℝN. Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.