We investigate blow-up solutions of the equation Δu = f(u) in a bounded smooth domain Ω ⊂ RN. Under appropriate growth conditions on f(t) as t goes to infinity we show how the mean curvature of the boundary ∂Ω appears in the second order term of the asymptotic expansion of the solution u(x) as x goes to ∂Ω.
Second order estimates for boundary blow-up solutions of elliptic equations
ANEDDA, CLAUDIA;
2007-01-01
Abstract
We investigate blow-up solutions of the equation Δu = f(u) in a bounded smooth domain Ω ⊂ RN. Under appropriate growth conditions on f(t) as t goes to infinity we show how the mean curvature of the boundary ∂Ω appears in the second order term of the asymptotic expansion of the solution u(x) as x goes to ∂Ω.
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