We find a second order approximation of the boundary blow-up solution of the equation \Delta u = e^{u |u|^{\beta -1}}, with \beta > 0, in a bounded smooth domain \Omega \subset R^N. Furthermore, we consider the equation \Delta u = e^{u+e^u}. In both cases we underline the effect of the geometry of the domain in the asymptotic expansion of the solutions near the boundary \partial \Omega.
Second-order estimates for boundary blow-up solutions of special elliptic equations
ANEDDA, CLAUDIA;
2006-01-01
Abstract
We find a second order approximation of the boundary blow-up solution of the equation \Delta u = e^{u |u|^{\beta -1}}, with \beta > 0, in a bounded smooth domain \Omega \subset R^N. Furthermore, we consider the equation \Delta u = e^{u+e^u}. In both cases we underline the effect of the geometry of the domain in the asymptotic expansion of the solutions near the boundary \partial \Omega.
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