Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: BMO solvability and absolute continuity of harmonic measure   We show that for a uniformly elliptic divergence form operator $L$, defined
in an open set $\Omega$ with Ahlfors-David regular boundary, BMO-solvability
implies scale invariant quantitative absolute continuity (the weak-$A_\infty$
property) of elliptic-harmonic measure with respect to surface measure on
$\partial \Omega$. We do not impose any connectivity hypothesis, qualitative or
quantitative; in particular, we do not assume the Harnack Chain condition, even
within individual connected components of $\Omega$. In this generality, our
results are new even for the Laplacian. Moreover, we obtain a converse, under
the additional assumption that $\Omega$ satisfies an interior Corkscrew
condition, in the special case that $L$ is the Laplacian.

11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
18
The categories of this paper are: econ
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg