Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase separation, optimal partitions, and nodal solutions to the Yamabe
  equation on the sphere   We study an optimal M-partition problem for the Yamabe equation on the round
sphere, in the presence of some particular symmetries. We show that there is a
correspondence between solutions to this problem and least-energy sign-changing
symmetric solutions to the Yamabe equation on the sphere with precisely M nodal
domains. The existence of an optimal partition is established through the study
of the limit profiles of least-energy solutions to a weakly coupled competitive
elliptic system on the sphere.

15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess