Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximum principles for boundary-degenerate linear parabolic differential
  operators   We develop weak and strong maximum principles for boundary-degenerate,
linear, parabolic, second-order partial differential operators, $Lu :=
-u_t-\tr(aD^2u)-\langle b, Du\rangle + cu$, with \emph{partial} Dirichlet
boundary conditions. The coefficient, $a(t,x)$, is assumed to vanish along a
non-empty open subset, $\mydirac_0!\sQ$, called the \emph{degenerate boundary
portion}, of the parabolic boundary, $\mydirac!\sQ$, of the domain
$\sQ\subset\RR^{d+1}$, while $a(t,x)$ may be non-zero at points in the
\emph{non-degenerate boundary portion}, $\mydirac_1!\sQ :=
\mydirac!\sQ\less\bar{\mydirac_0!\sQ}$. Points in $\mydirac_0!\sQ$ play the
same role as those in the interior of the domain, $\sQ$, and only the
non-degenerate boundary portion, $\mydirac_1!\sQ$, is required for boundary
comparisons. We also develop comparison principles and a priori maximum
principle estimates for solutions to boundary value and obstacle problems
defined by boundary-degenerate parabolic operators, again where only the
non-degenerate boundary portion, $\mydirac_1!\sQ$, is required for boundary
comparisons. Our results complement those in our previous articles
[arXiv1204.6613, arXiv:1305.5098].

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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: stat