The influence of domain geometry in the boundary behavior of large solutions of degenerate elliptic problems

Abstract

In this paper we study the asymptotic boundary behavior of large solutions of the equation $\Delta u=d^{\alpha }{u}^p$ in a regular bounded domain $\Omega$ in ${\mathbb{R}}^N$, $N\ge 2$, where $d(x)$ denotes the distance from $x$ to $\partial \Omega$, $p>1$ and $\alpha >0$. We precise the expansion which depends on the mean curvature of the boundary.