Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inequalities for eigenvalues of fourth order elliptic operators in
  divergence form on Riemannian manifolds   In this paper, we study eigenvalue of linear fourth order elliptic operators
in divergence form with Dirichlet boundary condition on a bounded domain in a
compact Riemannian manifolds with boundary (possibly empty) and find a general
inequality for them. As an application, by using this inequality, we study
eigenvalues of this operator on compact domains of complete submanifolds in a
Euclidean space.

27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph