Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the asymptotics of the principal eigenvalue for a Robin problem with
  a large parameter in planar domains   Let $\Omega\subset \RR^2$ be a domain having a compact boundary $\Sigma$
which is Lipschitz and piecewise $C^4$ smooth, and let $\nu$ denote the inward
unit normal vector on $\Sigma$. We study the principal eigenvalue $E(\beta)$ of
the Laplacian in $\Omega$ with the Robin boundary conditions $\partial
f/\partial\nu +\beta f=0$ on $\Sigma$, where $\beta$ is a positive number.
Assuming that $\Sigma$ has no convex corners we show the estimate
$E(\beta)=-\beta^2- \gamma_\mx\beta + O\big(\beta^\{2}{3}\big)$ as
$\beta\to+\infty$, where $\gamma_\mx$ is the maximal curvature of the boundary.

33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat