SMS scnews item created by Daniel Daners at Thu 22 Aug 2019 1424
Type: Seminar
Distribution: World
Expiry: 26 Aug 2019
Calendar1: 26 Aug 2019 1200-1300
CalLoc1: AGR Carslaw 829
CalTitle1: PDE Seminar: The Brunn-Minkowski inequality for the Monge-Ampere eigenvalue and smoothness of the eigenfunctions (Le)
Auth: daners@dora.maths.usyd.edu.au

PDE Seminar

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

Le

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 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.

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