Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poisson stochastic process and basic Schauder and Sobolev estimates in
  the theory of parabolic equations   We show among other things how knowing Schauder or Sobolev-space estimates
for the one-dimensional heat equation allows one to derive their
multidimensional analogs for equations with coefficients depending only on time
variable with the {\em same\/} constants as in the case of the one-dimensional
heat equation. The method is based on using the Poisson stochastic process. It
looks like no other method is available at this time and it is a very
challenging problem to find a purely analytic approach to proving such results.

20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess