Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Catenoidal layers for the Allen-Cahn equation in bounded domains   In this paper we present a new family of solutions to the singularly
perturbed Allen-Cahn equation $\alpha^2 \Delta u + u(1-u^2)=0, \quad \hbox{in
}\Omega\subset \R^N $ where $N=3$, $\Omega$ is a smooth bounded domain and
$\A>0$ is a small parameter. We provide asymptotic behavior which shows that,
as $\alpha \to 0$, the level sets of the solutions collapse onto a bounded
portion of a complete embedded minimal surface with finite total curvature that
intersects orthogonally $\partial \Omega$ of the domain and that is
non-degenerate respect to $\Omega$. We provide explicit examples of surfaces to
which our result applies.

1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn