Pointwise boundary behavior of large solutions to ∞-Laplacian equations

Abstract

We study the pointwise boundary behavior of the $\infty$-Laplacian problem

$${\mathrm{\Delta }}_{\infty }u=b(x)f(u),u\ge 0,x\in \mathrm{\Omega },u{|}_{\partial \mathrm{\Omega }}=\infty ,$$

where $b\in C(\overline{\mathrm{\Omega }})$ is positive in $\mathrm{\Omega }$, $f\in C[0,\infty )\cap C^1(0,\infty )$ is positive and nondecreasing on $(0,\infty )$ and satisfies an Keller–Osserman type condition.