Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp heat kernel estimates for spectral fractional Laplacian perturbed
  by gradient   By using Duhamel's formula, we prove sharp two-sided estimates for the heat
kernel of spectral fractional Laplacian with time-dependent gradient
perturbation in bounded $C^{1,1}$ domains. Moreover, we also obtain gradient
estimate as well as H\"older continuity of the gradient of the heat kernel.

13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph