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 c of the medium. We prove that all the eigenvalues, both simple and multiple, are locally Lip-schitz continuous with respect to c. Next, we show that simple eigenvalues and the symmetric functions of multiple eigenvalues depend real analytically upon c and we provide an explicit formula for their derivative in c. As an application of these results, we show that for a generic permittivity all the Maxwell eigenvalues are simple. (c) 2022 Elsevier Inc. All rights reserved.