On the Discreteness of Transmission Eigenvalues for the Maxwell Equations

In this paper, we establish the discreteness of transmission eigenvalues for Maxwell's equations. More precisely, show that spectrum eigenvalue problem is discrete if electromagnetic parameters $\varepsilon, \, \mu, \hat \varepsilon, \mu$ in equations characterizing inhomogeneity and background are smooth some neighborhood boundary isotropic on boundary, satisfy conditions $\varepsilon \neq \varepsilon$, $\mu \mu$, $\varepsilon/ \mu \varepsilon/ boundary. These quite general assumptions coefficients, which easy to check. To our knowledge, paper first without assuming any restrictions sign combination contrasts $\varepsilon-\hat \varepsilon$ - near allowing all be inhomogeneous anisotropic, except where they but not necessarily constant as often assumed literature.