Uniqueness and Layer Analysis for Boundary Blow-up Solutions

Abstract

We prove uniqueness for boundary blow-up solutions of the problem:Δu=λf(u) in Ω,u|∂Ω=∞, with large λ. Previous uniqueness results require a monotonicity assumption for f(u)lu in the entire range of the boundary blow-up solutions. By obtaining good boundary layer estimates for large λ, we obtain uniqueness under much weaker assumptions on f(u). Our estimates for the layers of the boundary blow-up solutions have independent interest, and may have other applications.