The Monge-Ampere equation appears naturally in various areas of mathematics. It consists in finding a convex function whose determinant of the Hessian is a prescribed nonnegative function f. The global estimates for the Monge-Ampere equation in the ``nondegenerate" case when the right hand side f is bounded below by a positive constant were obtained independently by Krylov and Caffarelli-Nirenberg-Spruck. In my talk I will discuss certain global estimates when the right hand side f is allowed to degenerate to 0 on the boundary of the domain. As an application we will address the smoothness of the eigenfunction for the Monge-Ampere operator.