Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Harnack inequality and its application to nonlocal eigenvalue problems
  in unbounded domains   We prove the Harnack inequality for general nonlocal elliptic equations with
zero order terms. As an application we prove the existence of the principal
eigenvalue in general domains. Furthermore, we study the eigenvalue problem
associated to the existence of self-similar solutions to the parabolic problem
and provide estimates on the decay rate.

31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio