Electron. J. Diff. Equ., Vol. 2011 (2011), No. 51, pp. 1-19.

Second-order boundary estimates for solutions to singular elliptic equations in borderline cases

Claudia Anedda, Giovanni Porru

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.

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

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