Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of nonradial domains for overdetermined and isoperimetric
  problems in nonconvex cones   In this work we address the question of the existence of nonradial domains
inside a nonconvex cone for which a mixed boundary overdetermined problem
admits a solution. Our approach is variational, and consists in proving the
existence of nonradial minimizers, under a volume constraint, of the associated
torsional energy functional. In particular we give a condition on the domain
$D$ on the sphere spanning the cone which ensures that the spherical sector is
not a minimizer. Similar results are obtained for the relative isoperimetric
problem in nonconvex cones.

18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess