Exact boundary behavior for the solutions to a class of infinity Laplace equations

摘要

In this paper, by Karamata regular variation theory and the method of lower and upper solutions, we give an exact boundary behavior for the unique solution near the boundary to the singular Dirichlet problem $ -Delta_{infty} u=b(x)g(u), u>0, x in Omega,$ $u|_{partial Omega}=0$, where $Omega$ is a bounded domain with smooth boundary in $mathbb{R}^N$, $gin C^1((0,infty), (0,infty))$, $g$ is decreasing on $(0,infty)$ and the function $b in C(ar{Omega})$ which is positive in $Omega$. We find a new structure condition on $g$ which plays a crucial role in the boundary behavior of the solutions.