Asymptotic estimates of boundary blow-up solutions to the infinity Laplace equations.

Abstract: In this paper we study the asymptotic behavior of boundary blow-up solutions to the equation in Ω, where is the ∞-Laplacian, the nonlinearity f is a positive, increasing function in , and the weighted function is positive in Ω and may vanish on the boundary. We first establish the exact boundary blow-up estimates with the first expansion when f is regularly varying at infinity with index and the weighted function b is controlled on the boundary in some manner. Furthermore, for the case of , with the function g normalized regularly varying with index , we obtain the second expansion of solutions near the boundary. It is interesting that the second term in the asymptotic expansion of boundary blow-up solutions to the infinity Laplace equation is independent of the geometry of the domain, quite different from the boundary blow-up problems involving the classical Laplacian. [Copyright &y& Elsevier]