The Order of Plurisubharmonicity on Pseudoconvex Domains with Lipschitz Boundaries

Abstract

Let $\Omega\subset\subset\mathbb{C}^n$ be a bounded pseudoconvex domain with Lipschitz boundary. Diederich and Fornaess have shown that when the boundary of $\Omega$ is $C^2$, there exists a constant $0<\eta<1$ and a defining function $\rho$ for $\Omega$ such that $-(-\rho)^{\eta}$ is a plurisubharmonic function on $\Omega$. In this paper, we show that the result of Diederich and Fornaess still holds when the boundary is only Lipschitz.