The Smoothness of the Eigenfunction for the Monge-Ampere Operator

Monday, November 2, 2015 - 2:00pm - 3:00pm
Keller 3-180
Ovidiu Savin (Columbia University)
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.
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