Boundary regularity of the solution to the complex Monge-Ampere equation on pseudoconvex domains of infinite type

摘要

Let Omega be a C-2-smooth, bounded, pseudoconvex domain in C-n satisfying the "f-property". The f-property is a consequence of the geometric "type" of the boundary. All pseudoconvex domains of finite type satisfy the f-property as well as many classes of domains of infinite type. In this paper, we prove the existence, uniqueness, and "weak" Holder-regularity up to the boundary of the solution to the Dirichlet problem for the complex Monge-Ampere equation