We investigate boundary blow-up solutions of the equation \Delta u = f(u) in a bounded smooth domain \Omega \subset R^N: Under the condition that f(t) grows exponentially as t goes to infinity we show how the mean curvature of the boundary \partial \Omega appears in the asymptotic expansion of the solution u(x) in terms of the distance of x from the boundary \partial \Omega.
Estimates for boundary blow-up solutions of semilinear elliptic equations
ANEDDA, CLAUDIA;
2008-01-01
Abstract
We investigate boundary blow-up solutions of the equation \Delta u = f(u) in a bounded smooth domain \Omega \subset R^N: Under the condition that f(t) grows exponentially as t goes to infinity we show how the mean curvature of the boundary \partial \Omega appears in the asymptotic expansion of the solution u(x) in terms of the distance of x from the boundary \partial \Omega.
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