Curl curl versus Dirichlet Laplacian eigenvalues
Spectral Theory
2025-05-22 v2 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.2404.11301,
title = {Curl curl versus Dirichlet Laplacian eigenvalues},
author = {Jonathan Rohleder},
journal= {arXiv preprint arXiv:2404.11301},
year = {2025}
}