Electron. J. Diff. Eqns., Vol. 2009(2009), No. 90, pp. 1-15.

Second-order boundary estimates for solutions to singular elliptic equations

Claudia Anedda

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.

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Claudia Anedda
Dipartimento di Matematica e Informatica
Universitá di Cagliari
Via Ospedale 72, 09124 Cagliari, Italy
email: canedda@unica.it

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