The second order expansion of boundary blow-up solutions for infinity-Laplacian equations

In this paper, by using Karamata regular variation theory and a perturbed argument, we study the second order expansion of viscosity solutions to boundary blow-up elliptic problem Δ∞u=b(x)f(u), x∈Ω, u|∂Ω=+∞, where Ω is a bounded domain with C2-boundary in RN, b∈C(Ω¯) is non-negative and non-trivial in Ω, f∈C1([0,∞)) is a normalized regularly varying function at infinity with index γ>3.