Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds for eigenvalue ratios of the Laplacian   For a bounded domain $\Omega$ with a piecewise smooth boundary in an
$n$-dimensional Euclidean space $\mathbf{R}^{n}$, we study eigenvalues of the
Dirichlet eigenvalue problem of the Laplacian. First we give a general
inequality for eigenvalues of the Laplacian. As an application, we study lower
order eigenvalues of the Laplacian and derive the ratios of lower order
eigenvalues of the Laplacian.

18
The categories of this paper are: econ
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg