Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Localization of eigenfunctions in a thin domain with locally periodic
  oscillating boundary   We study a Dirichlet spectral problem for a second-order elliptic operator
with locally periodic coefficients in a thin domain. The boundary of the domain
is assumed to be locally periodic. When the thickness of the domain
$\varepsilon$ tends to zero, the eigenvalues are of order $\varepsilon^{-2}$
and described in terms of the first eigenvalue $\mu(x_1)$ of an auxiliary
spectral cell problem parametrized by $x_1$, while the eigenfunctions localize
with rate $\sqrt{\varepsilon}$.

37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th