  Let $\Omega$ be an open set with Ahlfors-David regular boundary satisfying
the corkscrew condition. When $\Omega$ is connected in some quantitative form
one can establish that for any real elliptic operator with bounded
coefficients, the quantitative absolute continuity of elliptic measures is
equivalent to the fact that all bounded null solutions satisfy Carleson measure
estimates. In turn, in the same setting these equivalent properties are stable
under Fefferman-Kenig-Pipher perturbations. However, without connectivity,
there is no Fefferman-Kenig-Pipher perturbation result available. In this
paper, we work with a corona decomposition associated with the elliptic measure
and show that it is equivalent to the fact that bounded null solutions satisfy
partial/weak Carleson measure estimates, or to the fact that the Green function
is comparable to the distance to the boundary in the corona sense. This
characterization has profound consequences. We extend Fefferman-Kenig-Pipher's
perturbation to non-connected settings. For the Laplacian, these corona
decompositions or, equivalently, the partial/weak Carleson measure estimates
are meaningful enough to characterize the uniform rectifiability of the
boundary. As a consequence, we obtain that the boundary of the set is uniformly
rectifiable if bounded null solutions for any Fefferman-Kenig-Pipher
perturbation of the Laplacian satisfy Carleson measure estimates. For
Kenig-Pipher operators any of the properties of the characterization is stable
under transposition or symmetrization of the matrices of coefficients. As a
result, we obtain that Carleson measure estimates for bounded null-solutions of
non-symmetric variable operators satisfying an $L^1$-Kenig-Pipher condition
occur if and only if the boundary of the open set is uniformly rectifiable. Our
results generalize previous work in settings where quantitative connectivity.
