Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 51, pp. 1-19.

Title: Second-order boundary estimates for solutions to singular
       elliptic equations in borderline cases
       
Authors: Claudia Anedda (Univ. di Cagliari, Italy)
         Giovanni Porru (Univ. di Cagliari, Italy)

Abstract:
 Let $\Omega\subset R^N$ be a bounded smooth domain.
 We investigate the effect of the mean curvature of the boundary
 $\partial\Omega$ on the behaviour of the solution to the homogeneous
 Dirichlet boundary value problem for the equation $\Delta u+f(u)=0$.
 Under appropriate growth conditions on $f(t)$ as $t$ approaches zero,
 we find asymptotic expansions up to the second order of the solution
 in terms of the distance from  $x$ to the boundary $\partial\Omega$.

Submitted January 10, 2011. Published April 13, 2011.
Math Subject Classifications: 35B40, 35J67.
Key Words: Elliptic problems; singular equations; 
           second order boundary approximation.