Curl curl versus Dirichlet Laplacian eigenvalues

Jonathan Rohleder

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arXiv · 2404.11301

Curl curl versus Dirichlet Laplacian eigenvalues

Jonathan Rohleder

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Abstract

We provide an upper estimate for the eigenvalues of the curl curl operator on a bounded, three-dimensional Euclidean domain in terms of eigenvalues of the Dirichlet Laplacian. The result complements recent inequalities between curl curl and Neumann Laplacian eigenvalues. The curl curl eigenvalues considered here correspond to the Maxwell eigenvalue problem with constant material parameters.

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Jonathan Rohleder. 2024-04-17. Curl curl versus Dirichlet Laplacian eigenvalues. https://arxiv.org/abs/2404.11301

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