Second order estimates for large solutions of elliptic equations

This paper deals with the second term asymptotic behavior of large solutions to the problems Δu=b(x)f(u)Δu=b(x)f(u), x∈Ωx∈Ω, subject to the singular boundary condition u(x)=∞u(x)=∞, x∈∂Ωx∈∂Ω, where ΩΩ is a smooth bounded domain in RNRN, and b(x)b(x) is a non-negative weight function. The absorption term ff is regularly varying at infinite with index ρ>1ρ>1 (that is limu→∞f(ξu)/f(u)=ξρlimu→∞f(ξu)/f(u)=ξρ for every ξ>0ξ>0) and the mapping f(u)/uf(u)/u is increasing on (0,+∞)(0,+∞). Our analysis relies on the Karamata regular variation theory.