Hessian equations with Infinite Dirichlet Boundary Value

By Huaiyu Jian. 2006

66 citations recorded by the source corpus.

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.

View Paper: https://www.semanticscholar.org/paper/63863d8fc30b1c19b54e38ae46abeb5016a71457

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1. Xu-jia Wang
2. Neil S. Trudinger
3. Alessio Figalli
4. Bo Guan
5. Yanyan Li
6. Grégoire Loeper
7. S. Brendle
8. Huaihuo Cao

Citations in the corpus

• The k-Hessian Equation (2009, background): “where 0 • l J ,S,U3] (iv) Much more can be said about the regularity of the Monge-Ampµere equation.”