Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: A free boundary problem for semi-linear elliptic equation and its
  applications
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom