We investigate boundary blow-up solutions of the equation \Delta u = f (u) in a bounded domain Ω ⊂ R^N under the condition that f (t) has a relatively slow growth as t goes to infinity. We show how the mean curvature of the boundary ∂Ω appears in the asymptotic expansion of the solution u(x) in terms of the distance of x from ∂Ω.
Boundary behaviour for solutions of boundary blow-up problems in a borderline case
ANEDDA, CLAUDIA;
2009-01-01
Abstract
We investigate boundary blow-up solutions of the equation \Delta u = f (u) in a bounded domain Ω ⊂ R^N under the condition that f (t) has a relatively slow growth as t goes to infinity. We show how the mean curvature of the boundary ∂Ω appears in the asymptotic expansion of the solution u(x) in terms of the distance of x from ∂Ω.
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