Second order estimates for boundary blow-up solutions of elliptic equations

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2007, 2007(Special): 54-63. doi: 10.3934/proc.2007.2007.54

Second order estimates for boundary blow-up solutions of elliptic equations

Claudia Anedda ^1, and Giovanni Porru ^2,

1.	Dipartimento di Matematica e Informatica, Via Ospedale 72, 09124 Cagliari,, Italy
2.	Dipartimento di Matematica e Informatica, Via Ospedale 72, 09124 Cagliari, Italy

Received July 2006 Revised March 2007 Published September 2007

Abstract
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We investigate blow-up solutions of the equation $\Deltau$ = $f(u)$ in a bounded smooth domain $\Omega \subset R^N$. Under appropriate growth conditions on $f(t)$ as $t$ goes to infinity we show how the mean curvature of the boundary $\partial\Omega$ appears in the second order term of the asymptotic expansion of the solution $u(x)$ as $x$ goes to $\partial\Omega$.

Keywords: Blow-up solutions, Elliptic equations, Second order boundary estimates..

Mathematics Subject Classification: Primary: 35J25; Secondary: 35B05, 35B4.

Citation: Claudia Anedda, Giovanni Porru. Second order estimates for boundary blow-up solutions of elliptic equations. Conference Publications, 2007, 2007 (Special) : 54-63. doi: 10.3934/proc.2007.2007.54

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