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

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.