Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On shape optimization and the Pompeiu problem   The Pompeiu problem is considered as shape optimization problem. We show
stability of the ball which is the minimum point of related domain functional.
The proof is based on shape derivative method. Stability of the ball for
general domain functionals invariant under the rigid motions is discussed.

20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat