Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean value properties of solutions to the Helmholtz and modified
  Helmholtz equations   Mean value properties of solutions to the $m$-dimensional Helmholtz and
modified Helmholtz equations are considered. An elementary derivation of these
properties is given; it involves the Euler--Poisson--Darboux equation. Despite
the similar form of these properties for both equations, their consequences
distinguish essentially. The restricted mean value property for harmonic
functions is amended so that a function, satisfying it in a bounded domain of a
special class, solves the modified Helmholtz equation in this domain.

21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin