| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 21 | |
| Number of page(s) | 10 | |
| DOI | https://doi.org/10.1051/cocv/2025008 | |
| Published online | 20 March 2025 | |
A note on the failure of the Faber–Krahn inequality for the vector Laplacian
1
Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 12000 Prague 2, Czech Republic
2
Dipartimento di Tecnica e Gestione dei Sistemi Industriali (DTG), University of Padova, Stradella S. Nicola 3, 36100 Vicenza, Italy
3
Institut Fresnel, Aix-Marseille Université, Faculté des Sciences – Campus Saint Jérôme, Avenue Escadrille Normandie-Niémen, 13397 Marseille CEDEX, France
* Corresponding author: mic.zaccaron@gmail.com
Received:
9
October
2024
Accepted:
17
January
2025
We consider a natural eigenvalue problem for the vector Laplacian related to stationary Maxwell’s equations in a cavity and we prove that an analog of the celebrated Faber–Krahn inequality doesn’t hold, regardless of whether a volume or perimeter constraint is applied.
Mathematics Subject Classification: 35P15 / 35Q60 / 35Q61 / 35Q93 / 78M50
Key words: Maxwell’s equations / Hodge Laplacian / electromagnetic cavities / estimates for eigenvalues
© The authors. Published by EDP Sciences, SMAI 2025
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