Degenerate complex Monge-Ampère equations with non-Kähler forms in bounded domains (2303.04897v2)

Abstract: In this paper, we study weak solutions to complex Monge-Amp`ere equations of the form $(\omega + dd^c \varphi)^n= F(\varphi,.)d\mu$ on a bounded strictly pseudoconvex domain in $\mathbb{C}^n$, where $\omega$ is a smooth $(1,1)$-form, $0\leq F$ is a continuous non-decreasing function, and $\mu$ is a positive non-pluripolar measure. Our results extend previous works of Ko{\l}odziej and Nguyen \cite{KN15,KN23a,KN23b} who study bounded solutions, as well as Cegrell \cite{Ceg98,Ceg04,Ceg08}, Czy.z \cite{Cz09}, Benelkourchi \cite{Ben09,Ben15} and others who treat the case when $\omega=0$ and/or $F=1$.