logo_acta

Acta Mathematica Vietnamica

Complex Monge-Ampère Equation in Strictly Pseudoconvex Domains

icon-email Hoang-Son Do , Thai Duong Do , Hoang Hiep Pham

Abstract

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