Second-order boundary estimates for solutions to singular elliptic equations

Let $Omegasubset R^N$ be a bounded smooth domain. We investigate the effect of the mean curvature of the boundary $partialOmega$ in the behaviour of the solution to the homogeneous Dirichlet boundary value problem for the singular semilinear equation $Delta u+f(u)=0$. 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 $partialOmega$