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

Abstract

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 $1<p<N,0\le \mu <{\left((N-p)/p\right)}^p$ and $Q\in L^{\infty }({\mathbb{R}}^N)$. Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.

References in corpus (1)

• Asymptotic Behaviors of Solutions to quasilinear elliptic Equations with critical Sobolev growth and Hardy potential