Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-phase heat conductors with a stationary isothermic surface and their
  related elliptic overdetermined problems   We consider a two-phase heat conductor in two dimensions consisting of a core
and a shell with different constant conductivities. When the medium outside the
two-phase conductor has a possibly different conductivity, we consider the
Cauchy problem in two dimensions where initially the conductor has temperature
0 and the outside medium has temperature 1.
  It is shown that, if there is a stationary isothermic surface in the shell
near the boundary, then the structure of the conductor must be circular.
Moreover, as by-products of the method of the proof, we mention other proofs of
all the previous results of the author in $N(\ge 2)$ dimensions and two
theorems on their related two-phase elliptic overdetermined problems.

29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat