Weak solution of Parabolic complex Monge-Ampère equation

Abstract

We study the equation $\dot{u}=\log \det (u_{\alpha \bar{\beta }})-Au+f(z,t)$ in domains of ${\mathbb{C}}^n$. This equation has a close connection with the Kähler-Ricci flow. In this paper, we consider the case where the boundary condition is smooth and the initial condition is irregular.

arXiv comment27 pages, replacing the old 1.4 theorem (in 2nd version) by a slightly stronger result