Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Radial Limits of Bounded Nonparametric PMC Surfaces   Consider a solution $f\in C^{2}(\Omega)$ of a prescribed mean curvature
equation \[ {\rm div}\left(\frac{\nabla f}{\sqrt{1+|\nabla
f|^{2}}}\right)=2H(x,f) \ \ \ \ {\rm in} \ \ \Omega, \] where $\Omega\subset
\Real^{2}$ is a domain whose boundary has a corner at ${\cal
O}=(0,0)\in\partial\Omega.$ If $\sup_{x\in\Omega} |f(x)|$ and
$\sup_{x\in\Omega} |H(x,f(x))|$ are both finite and $\Omega$ has a reentrant
corner at ${\cal O},$ then the radial limits of $f$ at ${\cal O},$ \[
Rf(\theta) \myeq \lim_{r\downarrow 0} f(r\cos(\theta),r\sin(\theta)), \] are
shown to exist and to have a specific type of behavior, independent of the
boundary behavior of $f$ on $\partial\Omega.$ If $\sup_{x\in\Omega} |f(x)|$ and
$\sup_{x\in\Omega} |H(x,f(x))|$ are both finite and the trace of $f$ on one
side has a limit at ${\cal O},$ then the radial limits of $f$ at ${\cal O}$
exist and have a specific type of behavior.

9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph