Boundary Value Problems
Volume 2006 (2006), Article ID 45859, 12 pages
doi:10.1155/BVP/2006/45859

Second-order estimates for boundary blowup solutions of special elliptic equations

Claudia Anedda, Anna Buttu, and Giovanni Porru

Dipartimento di Matematica, Universitá di Cagliari, Via Ospedale 72, Cagliari 09124, Italy

Received 20 October 2005; Accepted 7 November 2005

Copyright © 2006 Claudia Anedda et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We find a second-order approximation of the boundary blowup solution of the equation Δu=eu|u|β−1, with β>0, in a bounded smooth domain Ω⊂RN. Furthermore, we consider the equation Δu=eu+eu. In both cases, we underline the effect of the geometry of the domain in the asymptotic expansion of the solutions near the boundary ∂Ω.