Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Sharp two-sided heat kernel estimates for critical Schr\"odinger
  operators on bounded domains
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom