VAPS 57:"Stationary solutions to the Bernoulli free boundary problem"

Speaker: Dennis Kriventsov, Rutgers
Abstract: Free boundary problems of Bernoulli type arise naturally in fluid dynamics, thermal models, shape optimization, and other contexts. We will focus on the simplest possible archetype problem, and consider many examples of solutions in one and two dimensions. Then we will look at the question of which kinds of solutions are closed under taking limits, and how those limits look like-this is a topic of practical importance for constructing solutions by any argument save for direct minimization. Thanks to a recent breakthrough in joint work with Georg Weiss, we can now give a very precise and descriptive answer to such questions.