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 ε of the medium. We prove that all the eigenvalues, both simple and multiple, are locally Lipschitz continuous with respect to ε. Next, we show that simple eigenvalues and the symmetric functions of multiple eigenvalues depend real analytically upon ε and we provide an explicit formula for their derivative in ε. As an application of these results, we show that for a generic permittivity all the Maxwell eigenvalues are simple.