Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-divergence Parabolic Equations of Second Order with Critical Drift
  in Morrey Spaces   We consider uniformly parabolic equations and inequalities of second order in
the non-divergence form with drift
\[-u_{t}+Lu=-u_{t}+\sum_{ij}a_{ij}D_{ij}u+\sum b_{i}D_{i}u=0\,(\geq0,\,\leq0)\]
in some domain $\Omega\subset \mathbb{R}^{n+1}$.
  We prove a variant of Aleksandrov-Bakelman-Pucci-Krylov-Tso estimate with
$L^{p}$ norm of the inhomogeneous term for some number $p<n+1$. Based on it, we
derive the growth theorems and the interior Harnack inequality. In this paper,
we will only assume the drift $b$ is in certain Morrey spaces defined below
which are critical under the parabolic scaling but not necessarily to be
bounded. This is a continuation of the work in \cite{GC}.

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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph