Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogenization of Poisson and Stokes equations in the whole space   We consider the homogenization of the Poisson and the Stokes equations in the
whole space perforated with periodically distributed small holes. The periodic
homogenization in bounded domains is well understood, following the classical
results in [24, 4, 1, 2]. In this paper, we show that these classical
homogenization results in a bounded domain can be extended to the whole space
${\mathbb R}^d$. Our results cover all three cases corresponding to different
sizes of holes and cover all $d\geq 2$.

29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex