Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence results for nonlocal problems governed by the regional
  fractional Laplacian   The aim of the present paper is to study existence results of minimizers of
the critical fractional Sobolev constant on bounded domains. Under some values
of the fractional parameter we show that the best constant is achieved. If
moreover the underlying domain is a ball, we obtain positive radial minimizers
for all possible values of the fractional parameter in higher dimension, while
we impose a positive mass condition in low dimension.

17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ