Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probabilistic representations of solutions of elliptic boundary value
  problem and non-symmetric semigroups   In this paper, we use a probabilistic approach to show that there exists a
unique, bounded continuous solution to the Dirichlet boundary value problem for
a general class of second order non-symmetric elliptic operators $L$ with
singular coefficients, which does not necessarily have the maximum principle.
The theory of Dirichlet forms and heat kernel estimates play a crucial role in
our approach. A probabilistic representation of the non-symmetric semigroup
$\{T_t\}_{t\ge 0}$ generated by $L$ is also given.

11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom