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arXiv · 2202.00511

A few results on permittivity variations in electromagnetic cavities

Paolo Luzzini·Michele Zaccaron
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Abstract

We study the eigenvalues of time-harmonic Maxwell's equations in a cavity upon changes in the electric permittivity $\varepsilon$ of the medium. We prove that all the eigenvalues, both simple and multiple, are locally Lipschitz continuous with respect to $\varepsilon$. Next, we show that simple eigenvalues and the symmetric functions of multiple eigenvalues depend real analytically upon $\varepsilon$ and we provide an explicit formula for their derivative in $\varepsilon$. As an application of these results, we show that for a generic permittivity all the Maxwell eigenvalues are simple.

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Paolo Luzzini, Michele Zaccaron. 2022-02-01. A few results on permittivity variations in electromagnetic cavities. https://doi.org/10.1016/j.jde.2022.06.023

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