PDEA Seminar: Inequalities between Neumann and Dirichlet Laplacian eigenvalues

Abstract: Non-trivial inequalities between Neumann and Dirichlet Laplacian eigenvalues have a long history going back at least to work of Pólya and Payne in the 1950s, followed by significant contributions by Levine and Weinberger, Friedlander, Filonov, and others. In this talk, some recent developments around the topic are presented. In particular, we show that an optimal inequality proven by Levine and Weinberger for convex domains remains true for simply connected planar domains.

This is a seminar in the PDEs and Applications seminar series.