Seminars & Colloquia Calendar
Spectral Optimization and Free Boundary Problems
Dennis Kriventsov, New York University
Location: Hill 705
Date & time: Wednesday, 31 January 2018 at 12:00PM - 1:00PM
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.