The Brunn-Minkowski inequality for the Monge-Ampere eigenvalue and smoothness of the eigenfunctions

Nam Quang Le
Indiana University, USA
Mon 26th Aug 2019, 12-1pm, Carslaw Room 829 (AGR)

Abstract

The original form of the Brunn-Minkowski inequality involves volumes of convex bodies in ${ℝ}^n$ and states that the $n$-th root of the volume is a concave function with respect to the Minkowski addition of convex bodies.

In 1976, Brascamp and Lieb proved a Brunn-Minkowski inequality for the first eigenvalue of the Laplacian. In this talk, I will discuss a nonlinear analogue of the above result, that is, the Brunn-Minkowski inequality for the eigenvalue of the Monge-Ampère operator. For this purpose, I will first introduce the Monge-Ampère eigenvalue problem on general bounded convex domains. Then, I will present several properties of the eigenvalues and related analysis concerning smoothness of the eigenfunctions.

For Seminar announcements you can now subscribe to the Seminar RSS feed. Check also the PDE Seminar page.

Enquiries to Daniel Hauer or Daniel Daners.