Second-order boundary estimates for solutions to singular elliptic equations

Let ω ⊂ R N be a bounded smooth domain. We investigate the effect of the mean curvature of the boundary ∂ω in the behaviour of the solution to the homogeneous Dirichlet boundary value problem for the singular semilinear equation δu + f(u) = 0. Under appropriate growth conditions on f(t) as t approaches zero, we find an asymptotic expansion up to the second order of the solution in terms of the distance from x to the boundary ∂ ω .