Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Thermal approximation of the equilibrium measure and obstacle problem
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con