Hessian Equations with infinite Dirichlet boundary value

Details Hessian Equations with infinite Dirichlet boundary value Hessian Equations with infinite Dirichlet boundary value

2006-11-29

arxiv.org/abs/math/0611907v1

Indiana University Mathematics Journal Vol 55, No 3, 2006

Mathematics

Analysis of PDEs

17pages

Scientific paper

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.

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