Second order estimates for boundary blowup solutions of quasilinear elliptic equations

Abstract

Let Ω⊂RN be a bounded smooth domain. We investigate the effect of the mean curvature of the boundary ∂Ω on the behavior of the blow-up solution to the equation Δu=up|∇u|q. Under appropriate conditions on p and q, we find asymptotic expansions up to the second order of the solution u in terms of the distance from x to the boundary ∂Ω.