The complex Monge-Ampère equation on weakly pseudoconvex domains

Abstract

We show here a "weak" Hölder-regularity up to the boundary of the solution to the Dirichlet problem for the complex Monge-Ampère equation with data in the $L^p$ space and the boundary of the domain satisfying an $f$-property. The $f$-property is a potential-theoretical condition which holds for all pseudoconvex domains of finite type and many examples of infinite type.

final version