Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global heat kernel estimates for symmetric Markov processes dominated by
  stable-like processes in exterior $C^{1,\eta}$ open sets   In this paper, we establish sharp two-sided heat kernel estimates for a large
class of symmetric Markov processes in exterior $C^{1,\eta}$ open sets for all
$t> 0$. The processes are symmetric pure jump Markov processes with jumping
kernel intensity $$\kappa(x, y)\psi(|x-y|)^{-1}|x-y|^{-d-\alpha}$$ where
$\alpha\in(0,2)$, $\psi$ is an increasing function on $[ 0, \infty)$ with
$\psi(r)=1$ on $0<r\le 1$ and $c_1e^{c_2r^{\beta}}\le \psi(r)\le
c_3e^{c_4r^{\beta}}$ on $r>1$ for $\beta\in[0, \infty]$. A symmetric function
$\kappa(x, y)$ is bounded by two positive constants and $|\kappa(x,
y)-\kappa(x,x)|\le c_5 |x-y|^{\rho}$ for $|x-y|<1$ and $\rho>\alpha/2$. As a
corollary of our main result, we estimates sharp two-sided Green function for
this process in $C^{1,\eta}$ exterior open sets.

13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph