EVENT DETAILS AND ABSTRACT

Title: Regularity for Spectral Optimizers
Speaker: Dennis Krivensov
Speaker Info: Courant Institute
Brief Description: TBA
Special Note:
Abstract:

A classic subject in analysis is the relationship between the spectrum of the Laplacian on a domain and that domain's geometry. One approach to understanding this relationship is to study domains which extremize some function of their spectrum under geometric constraints. I will explain how to attack these problems using tools from the calculus of variations to find solutions. A key difficulty with this method is showing that the optimizers (which are a priori very weak) are actually smooth domains, and I address this issue in some recent work with Fanghua Lin. Our results are based on relating spectral optimization problems to certain vector-valued free boundary problems of Bernoulli type.