Boundary behaviour of the unique solution to a singular Dirichlet problem with a convection term

Abstract

By Karamata regular variation theory and constructing comparison functions, we derive that the boundary behaviour of the unique solution to a singular Dirichlet problem − Δ u = b ( x ) g ( u ) + λ | ∇ u | q , u > 0 , x ∈ Ω , u | ∂ Ω = 0 , which is independent of λ | ∇ u λ | q , where Ω is a bounded domain with smooth boundary in R N , λ ∈ R , q ∈ ( 0 , 2 ] , lim s → 0 + g ( s ) = + ∞ , and b is non-negative on Ω, which may be vanishing on the boundary.