Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Applications of elliptic operator theory to the isotropic interior
  transmission eigenvalue problem   The paper concerns the isotropic interior transmission eigenvalue (ITE)
problem. This problem is not elliptic, but we show that, using the
Dirichlet-to-Neumann map, it can be reduced to an elliptic one. This leads to
the discreteness of the spectrum as well as to certain results on possible
location of the transmission eigenvalues. If the index of refraction
$\sqrt{n(x)}$ is real, we get a result on the existence of infinitely many
positive ITEs and the Weyl type lower bound on its counting function. All the
results are obtained under the assumption that $n(x)-1$ does not vanish at the
boundary of the obstacle or it vanishes identically, but its normal derivative
does not vanish at the boundary. We consider the classical transmission problem
as well as the case when the inhomogeneous medium contains an obstacle. Some
results on the discreteness and localization of the spectrum are obtained for
complex valued $n(x)$.

10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an