Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Separation of a Lower Dimensional Free Boundary in a Two Phase Problem   This paper studies local properties of a two phase free boundary problem for
the fractional Laplacian. The main result states that the two free boundaries
of the positive and negativity sets cannot touch.

9
The categories of this paper are: nlin
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat