Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Free Material Design problem for stationary heat equation on low
  dimensional structures   For a given balanced distribution of heat sources and sinks, $Q$, we find an
optimal conductivity tensor field, $\hat C$, minimizing the thermal compliance.
We present $\hat C$ in a rather explicit form in terms of the datum. Our
solution is in a cone of non-negative tensor-valued finite Borel measures. We
present a series of examples with explicit solutions.49J20, %Singular parabolic
equations secondary: 49K20, 80M50

8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn