Curl curl versus Dirichlet Laplacian eigenvalues

2024/04/17 by Jonathan Rohleder, Rohleder, Jonathan · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2404.11301

openalex publication_date 2024/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Trapped modes in electromagnetic waveguides

Related

• Spectral geometry of the curl operator on smoothly bounded domains
• The Isoperimetric Problem for the Curl Operator
• Approximation of the Maxwell eigenvalue problem in a Least-Squares setting
• Computational lower bounds of the Maxwell eigenvalues
• On Maxwell's and Poincare's Constants