A few results on permittivity variations in electromagnetic cavities

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.