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.