Acta Mathematica Vietnamica
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Complex Monge-Ampère Equation in Strictly Pseudoconvex Domains
Hoang-Son Do , Thai Duong Do , Hoang Hiep Phampp. 93-101
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”.