Daniel Peralta-Salas (ICMAT)

Title: Optimal domains for the first curl eigenvalue
Abstract: The classical Faber-Krahn inequality for the first eigenvalue of the Dirichlet Laplacian shows that the ball is the unique optimal domain. In this talk I will explore the analogous problem for the curl operator: for a fixed volume, what is the optimal domain for the first positive (or negative) eigenvalue of curl? In spite of being one of the most important vector-valued operators, this question is rather unexplored and remains wide open. In this talk I will show that, even taking into account that the first eigenvalue is uniformly lower bounded in terms of the volume, there are no axisymmetric smooth optimal domains for the curl that satisfy a mild technical assumption. In particular, this rules out the existence of optimal axisymmetric domains with a convex section. This is based on joint work with Alberto Enciso.

For more Zoom meeting information please contact dmitry.jakobson [at] mcgill.ca