Second order estimates for boundary blow-up solutions of elliptic equations with an additive gradient term

Let Ω⊂RNΩ⊂RN be a bounded smooth domain and let 0≤ℓ≤10≤ℓ≤1, p>1p>1. We investigate the effect of the mean curvature of the boundary ∂Ω∂Ω on the behavior of the solution to the problem Δu−ℓ|Du|2pp+1=up in ΩΩ, u=∞u=∞ on ∂Ω∂Ω. We find an asymptotic expansion up to the second order of the solution uu in terms of the distance from xx to the boundary ∂Ω∂Ω.