Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Liouville theorems and optimal regularity in elliptic equations
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat