A few results on permittivity variations in electromagnetic cavities

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