Title: Hessian equations with infinite Dirichlet boundary

Authors: Huaiyu Jian

Issue: Volume 55 (2006), Issue 3, 1045-1062

Abstract: In this paper, we study the Hessian equation with infinite Dirichlet (blow-up) boundary value conditions. Using radial functions and techniques of ordinary differential inequality, we construct various barrier functions (super-solution and sub-solution). Existence and non-existence theorems are proved by those barriers, maximum principle and theory of viscous solutions. Furthermore, generic boundary blow-up rates for the solutions are derived.