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

Pages: 54 - 63, Issue Special, September 2007

 Abstract        Full Text (193.7K)              

Claudia Anedda - Dipartimento di Matematica e Informatica, Via Ospedale 72, 09124 Cagliari,, Italy (email)
Giovanni Porru - Dipartimento di Matematica e Informatica, Via Ospedale 72, 09124 Cagliari, Italy (email)

Abstract: 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:  Elliptic equations, Blow-up solutions, Second order boundary estimates.
Mathematics Subject Classification:  Primary: 35J25; Secondary: 35B05, 35B40.

Received: July 2006;      Revised: March 2007;      Published: September 2007.