Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Matzoh ball soup revisited: the boundary regularity issue   We consider nonlinear diffusion equations of the form $\partial_t u= \Delta
\phi(u)$ in $\mathbb R^N$ with $N \ge 2.$ When $\phi(s) \equiv s$, this is just
the heat equation. Let $\Omega$ be a domain in $\mathbb R^N$, where
$\partial\Omega$ is bounded and $\partial\Omega = \partial (\mathbb
R^N\setminus \bar {\Omega})$. We consider the initial-boundary value problem,
where the initial value equals zero and the boundary value equals 1, and the
Cauchy problem where the initial data is the characteristic function of the set
$\Omega^c = \mathbb R^N\setminus \Omega$. We settle the boundary regularity
issue for the characterization of the sphere as a stationary level surface of
the solution $u:$ no regularity assumption is needed for $\partial\Omega.$

8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
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The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an