Asymptotic behavior and uniqueness results for boundary blow-up solutions

Abstract

We estimate the blow-up rate and then improve some existing uniqueness results for boundary blow-up solutions to certain quasilinear elliptic equations with a weight function. The weight function is allowed to vanish on the part of the boundary where the solution blows up. Our approach is based on the construction of certain upper and lower solutions on small annuli with partial boundary blow-up, and on a modified version of an iteration technique due to Safonov.