Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of two-phase shape optimization problems by means of shape
  derivatives   This is my Ph.D. Thesis at Tohoku Univeristy (July 2018). It presents the
theory on shape derivatives and focuses on its applications to two-phase
optimization problems. In particular, we treat the two-phase torsion problem
and a two-phase analogous of Serrin's overdetermined problem.

11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg