Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A singularly perturbed Dirichlet problem for the Poisson equation in a
  periodically perforated domain. A functional analytic approach   Let $\Omega$ be a sufficiently regular bounded open connected subset of
$\mathbb{R}^n$ such that $0 \in \Omega$ and that $\mathbb{R}^n \setminus
\mathrm{cl}\Omega$ is connected. Then we take $(q_{11},\dots, q_{nn})\in
]0,+\infty[^n$ and $p \in Q\equiv \prod_{j=1}^{n}]0,q_{jj}[$. If $\epsilon$ is
a small positive number, then we define the periodically perforated domain
$\mathbb{S}[\Omega_{p,\epsilon}]^{-} \equiv \mathbb{R}^n\setminus \cup_{z \in
\mathbb{Z}^n}\mathrm{cl}\bigl(p+\epsilon \Omega +\sum_{j=1}^n
(q_{jj}z_j)e_j\bigr)$, where $\{e_1,\dots,e_n\}$ is the canonical basis of
$\mathbb{R}^n$. For $\epsilon$ small and positive, we introduce a particular
Dirichlet problem for the Poisson equation in the set
$\mathbb{S}[\Omega_{p,\epsilon}]^{-}$. Namely, we consider a Dirichlet
condition on the boundary of the set $p+\epsilon \Omega$, together with a
periodicity condition. Then we show real analytic continuation properties of
the solution as a function of $\epsilon$, of the Dirichlet datum on $p+\epsilon
\partial \Omega$, and of the Poisson datum, around a degenerate triple with
$\epsilon=0$.

29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics