Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional one-sided measure theoretic second-order elliptic operators
  and applications to stochastic partial differential equations   In this work we introduce and study fractional measure theoretic elliptic
operators on the torus and a new stochastic process named W-Brownian motion. We
establish some regularity and spectral results related to the operators cited
above, more precisely, we were able to provide sharp bounds for the growth rate
of eigenvalues to an associated eigenvalue problem. Moreover, we show how the
Cameron-Martin space associated to the W-Brownian motion relates to Sobolev
spaces connected with the elliptic operators mentioned above. Finally
applications of the theory developed on stochastic partial differential
equations are given.

8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci