Exact asymptotic behavior near the boundary to the solution for singular nonlinear Dirichlet problems

Abstract

We take up the existence and the exact asymptotic behavior near the boundary ∂ Ω of the unique classical solution to a singular Dirichlet problem − Δ u = a ( x ) g ( u ) , x ∈ Ω , u > 0 in Ω , u ∣ ∂ Ω = 0 , where Ω is a C 1 , 1 -bounded domain in R n , n ≥ 2 and the function a is singular near the boundary and belongs to the Kato class K ( Ω ) .