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

Date: 2024-06-10

Time: 11:20 - 12:10

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Jonathan Rohleder, Stockholm University

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.