Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-linear ground state representations and sharp Hardy inequalities   We determine the sharp constant in the Hardy inequality for fractional
Sobolev spaces. To do so, we develop a non-linear and non-local version of the
ground state representation, which even yields a remainder term. From the sharp
Hardy inequality we deduce the sharp constant in a Sobolev embedding which is
optimal in the Lorentz scale. In the appendix, we characterize the cases of
equality in the rearrangement inequality in fractional Sobolev spaces.

12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg