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.
A note on the failure of the Faber–Krahn inequality for the vector Laplacian
Lamberti, Pier Domenico;
2025
Abstract
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.
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