Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 90, pp. 1-15.

Title: Second-order boundary estimates for solutions to
       singular elliptic equations

Author: Claudia Anedda (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
 $\partial\Omega$ 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 $\partial\Omega$.
  
Submitted June 17, 2009. Published July 30, 2009.
Math Subject Classifications: 35B40, 35B05, 35J25.
Key Words: Elliptic problems; singular equations; 
           second order boundary approximation.