Dirichlet Problems of Monge-ampère Equations

This note presents a detailed and self-contained discussion of the Dirichlet problem of real Monge-Ampère equations in strictly convex domains and complex Monge-Ampère equations in strongly pseudo-convex domains. Sections 1.1 and 1.2 follow [2] and [3] respectively, while Sections 2.1, 2.2 and 2.3 are based on [5], [4] and [1] respectively. This note is written for lectures in the Special Lecture Series in Peking University in the summer of 2007. A part of it was presented in the Summer School on Geometric Analysis in the University of Science and Technology of China, July 2006.