Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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, we show that the spectrum of the
transmission eigenvalue problem is discrete, if the electromagnetic parameters
$\eps, \, \mu, \, \heps, \, \hmu$ in the equations characterizing the
inhomogeneity and background, are smooth in some neighborhood of the boundary,
isotropic on the boundary, and satisfy the conditions $\eps \neq \heps$, $\mu
\neq \hmu$, and $\eps/ \mu \neq \heps/ \hmu$ on the boundary. These are quite
general assumptions on the coefficients which are easy to check. To our
knowledge, our paper is the first to establish discreteness of transmission
eigenvalues for Maxwell's equations without assuming any restrictions on the
sign combination of the contrasts $\eps-\heps$ and $\mu - \hmu$ near the
boundary, and allowing for all the electromagnetic parameters to be
inhomogeneous and anisotropic, except for on the boundary where they are
isotropic but not necessarily constant as it is often assumed in the
literature.

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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: nlin