Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some symmetry results for entire solutions of an elliptic system arising
  in phase separation   We study the one dimensional symmetry of entire solutions to an elliptic
system arising in phase separation for Bose-Einstein condensates with multiple
states. We prove that any monotone solution, with arbitrary algebraic growth at
infinity, must be one dimensional in the case of two spatial variables. We also
prove the one dimensional symmetry for half-monotone solutions, i.e., for
solutions having only one monotone component.

23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs