Boundary behavior for the solutions to Dirichlet problems involving the infinity-Laplacian

In this paper, by constructing suitable comparison functions, we mainly analyze the exact boundary behavior for the unique solution near the boundary to the singular Dirichlet problem − Δ ∞ u = b ( x ) g ( u ) , u > 0 , x ∈ Ω , u | ∂ Ω = 0 , where Ω is a bounded domain with smooth boundary in R N , g ∈ C 1 ( ( 0 , ∞ ) , ( 0 , ∞ ) ) , g is decreasing on ( 0 , ∞ ) with lim s → 0 + ⁡ g ( s ) = ∞ , g is normalized regularly varying at zero with index −γ ( γ > 1 ) and b ∈ C ( Ω ¯ ) which is positive in Ω and may be vanishing on the boundary and rapidly varying near the boundary.