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

Abstract

All rights reserved. Let Ω be a C2-smooth, bounded, pseudoconvex domain in Cn satisfying the -property. The f -property is a consequence of the geometric 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 (Formula Presented) The idea of our proof goes back to Bedford and Taylor [1]. However, the basic geometrical ingredient is based on a recent result by Khanh [12].