Complex Monge-Ampère equation in strictly pseudoconvex domains

Abstract

We study the complex Monge-Ampère equation $(d{d}^{c}u{)}^n=\mu$ in a strictly pseudoconvex domain $\Omega$ with the boundary condition $u=\phi$, where $\phi \in C(\partial \Omega )$. We provide a non-trivial sufficient condition for continuity of the solution $u$ outside "small sets".

9 pages