Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform rectifiability and elliptic operators satisfying a Carleson
  measure condition   The present paper establishes the correspondence between the properties of
the solutions of a class of PDEs and the geometry of sets in Euclidean space.
We settle the question of whether (quantitative) absolute continuity of the
elliptic measure with respect to the surface measure and uniform rectifiability
of the boundary are equivalent, in an optimal class of divergence form elliptic
operators satisfying a suitable Carleson measure condition. The result can be
viewed as a quantitative analogue of the Wiener criterion adapted to the
singular $L^p$ data case.
  We split our proof on two main steps. In the first one we considered the case
in which the desired Carleson measure condition on the coefficients holds with
"sufficiently small constant", using a novel application of techniques
developed in geometric measure theory. In the second step we establish the
final result, that is, the "large constant case". The key elements are a
powerful extrapolation argument, which provides a general pathway to
self-improve scale-invariant small constant estimates, and a new mechanism to
transfer quantitative absolute continuity of elliptic measure between a domain
and its subdomains.

20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an