Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp pointwise estimates for the gradients of solutions to linear
  parabolic second order equation in the layer   We deal with solutions of the Cauchy problem to linear both homogeneous and
nonhomogeneous parabolic second order equations with real constant coefficients
in the layer ${\mathbb R}^{n+1}_T={\mathbb R}^n\times (0, T)$, where $n\geq 1$
and $T<\infty$. The homogeneous equation is considered with initial data in
$L^p({\mathbb R}^n)$, $1\leq p \leq \infty $. For the nonhomogeneous equation
we suppose that initial function is equal to zero and the function in the
right-hand side belongs to $f\in L^p({\mathbb R}^{n+1}_T)\cap C^\alpha \big
(\bar{{\mathbb R}^{n+1}_T} \big ) $ , $p>n+2$ and $\alpha \in (0, 1)$. Explicit
formulas for the sharp coefficients in pointwise estimates for the length of
the gradient to solutions to these problems are obtained.

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The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex