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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 $(d d^{c} u)^{n} = μ$ in a strictly pseudoconvex domain $Ω$ with the boundary condition $u = φ$ , where $φ \in C (\partial Ω)$ . We provide a non-trivial sufficient condition for continuity of the solution $u$ outside “small sets”.

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Complex Monge-Ampère Equation in Strictly Pseudoconvex Domains

Abstract