Jonathan Rohleder: Spectral inequalities for Laplacian and curl-curl eigenvalue

Speaker
Jonathan Rohleder, Stockholm University

Abstract
In 1955, Payne proved that below the k-th eigenvalue of the Dirichlet Laplacian on a planar bounded domain, there exist at least k+2 eigenvalues of the Neumann Laplacian, provided the domain is convex. We use a novel variational principle to extend this result to all simply connected planar Lipschitz domains. Furthermore, we derive similar inequalities for the curl curl operator in space dimension three.