We analyze the asymptotic behavior near the boundary of viscosity solutions to the singular problem \(\begin{aligned} \left\{ \begin{array}{ll} \Delta _\infty ^h u=-b(x)g(u) \quad & \textrm{in}\, \Omega , \\ u>0 \quad & \textrm{in}\, \Omega , \\ u=0 \quad & \textrm{on} \,\partial \Omega , \end{array}\right. \end{aligned}\) where \(h>1,\) \(\Delta _\infty ^h u=|Du|^{h-3}\Delta _\infty u \) and \(\Delta _\infty u=\langle D^2uDu,Du \rangle \) is the infinity Laplacian which is strongly degenerate, quasilinear and arising from the absolutely minimizing Lipschitz extension. Our main result concerns the case when the nonlinearity g is regularly varying at zero with index \(-h\) .
