Asymptotic Behavior of Solutions to a Doubly Weighted Quasi-linear Equation

Abstract

We establish pointwise asymptotic estimates at infinity for solutions to the doubly weighted quasi-linear equation: $$\{\begin{array}{rlrl}-\mathrm{div}(w_1|\mathrm{\nabla }u{|}^{p-2}\mathrm{\nabla }u)& =w_2|u{|}^{q-2}u& & \text{in }\mathrm{\Omega },\\ u\in D^{1,p,w_1}& (\mathrm{\Omega }),\end{array}$$ where $w_1$ and $w_2$ are compatible weights and $q>p>1$ is a critical exponent in the sense of Sobolev.