Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The nodal line of the second eigenfunction of the Robin Laplacian in
  $\mathbb{R}^2$ can be closed   We construct a multiply connected domain in $\mathbb{R}^2$ for which the
second eigenfunction of the Laplacian with Robin boundary conditions has an
interior nodal line. In the process, we adapt a bound of Donnelly-Fefferman
type to obtain a uniform estimate on the size of the nodal sets of a sequence
of solutions to a certain class of elliptic equations in the interior of a
sequence of domains, which does not depend directly on any boundary behaviour.
This also gives a new proof of the nodal line property of the example in the
Dirichlet case.

18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph