Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The fractional nonlocal Ornstein--Uhlenbeck equation, Gaussian
  symmetrization and regularity   For $0<s<1$, we consider the Dirichlet problem for the fractional nonlocal
Ornstein--Uhlenbeck equation $$\begin{cases}
(-\Delta+x\cdot\nabla)^su=f&\hbox{in}~\Omega\\ u=0&\hbox{on}~\partial\Omega,
\end{cases}$$ where $\Omega$ is a possibly unbounded open subset of
$\mathbb{R}^n$, $n\geq2$. The appropriate functional settings for this nonlocal
equation and its corresponding extension problem are developed. We apply
Gaussian symmetrization techniques to derive a concentration comparison
estimate for solutions. As consequences, novel $L^p$ and $L^p(\log L)^\alpha$
regularity estimates in terms of the datum $f$ are obtained by comparing $u$
with half-space solutions.

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The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: adap-org