Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimizers for the fractional Sobolev inequality on domains   We consider a version of the fractional Sobolev inequality in domains and
study whether the best constant in this inequality is attained. For the
half-space and a large class of bounded domains we show that a minimizer
exists, which is in contrast to the classical Sobolev inequalities in domains.

23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
1
The categories of this paper are: cs