Boundary behaviour for solutions of boundary blow-up problems in a borderline case

摘要

We investigate boundary blow-up solutions of the equation Δ 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.