Hessian equations with infinite Dirichlet boundary Huaiyu Jian 35A0535B0535K1535K5553C44Hessian equationk-convex solutionsingular boundary valueexistence/noexistenceviscous solution 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. Indiana University Mathematics Journal 2006 text pdf 10.1512/iumj.2006.55.2728 10.1512/iumj.2006.55.2728 en Indiana Univ. Math. J. 55 (2006) 1045 - 1062 state-of-the-art mathematics http://iumj.org/access/