On the Boundary Behaviour, Including Second Order Effects, of Solutions to Singular Elliptic Problems

Berhanu, S.; Cuccu, F.; Porru, G.
March 2007
Acta Mathematica Sinica;Mar2007, Vol. 23 Issue 3, p479
Academic Journal
For γ ≥ 1 we consider the solution u = u( x) of the Dirichlet boundary value problem Δ u + u − γ = 0 in Ω, u = 0 on ∂Ω. For γ = 1 we find the estimate where $$ p{\left( r \right)} \approx r{\sqrt {2\log {\left( {1 \mathord{\left/ {\vphantom {1 r}} \right. \kern-\nulldelimiterspace} r} \right)}} } $$ near r = 0, δ( x) denotes the distance from x to ∂Ω, 0 < ∈ < 1/2, and A( x) is a bounded function. For 1 < γ < 3 we find For γ = 3 we prove that


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