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

摘要

For γ≥1 we consider the solution u=u(x) of the Dirichlet boundary value problemΔu+u^(-γ)=0 in Ω,u=0 on Ω.For γ=1 we find the estimate,where p(r)≈r(2 log(l/r))^(1/2) 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.