Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sobolev differentiable flows of SDEs with local Sobolev and super-linear
  growth coefficients   By establishing a characterization for Sobolev differentiability of random
fields, we prove the weak differentiability of solutions to stochastic
differential equations with local Sobolev and super-linear growth coefficients
with respect to the starting point. Moreover, we also study the strong Feller
property and the irreducibility of the associated diffusion semigroup.

1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org