  We generalize to the setting of 1-sided chord-arc domains, that is, to
domains satisfying the interior Corkscrew and Harnack Chain conditions (these
are respectively scale-invariant/quantitative versions of the openness and
path-connectedness) and which have an Ahlfors regular boundary, a result of
Kenig-Kirchheim-Pipher-Toro, in which Carleson measure estimates for bounded
solutions of the equation $Lu=-{\rm div}(A\nabla u) = 0$ with $A$ being a real
(not necessarily symmetric) uniformly elliptic matrix, imply that the
corresponding elliptic measure belongs to the Muckenhoupt $A_\infty$ class with
respect to surface measure on the boundary. We present two applications of this
result. In the first one we extend a perturbation result recently proved by
Cavero-Hofmann-Martell presenting a simpler proof and allowing non-symmetric
coefficients. Second, we prove that if an operator $L$ as above has locally
Lipschitz coefficients satisfying certain Carleson measure condition then
$\omega_L\in A_\infty$ if and only if $\omega_{L^\top}\in A_\infty$. As a
consequence, we can remove one of the main assumptions in the non-symmetric
case of a result of Hofmann-Martell-Toro and show that if the coefficients
satisfy a slightly stronger Carleson measure condition the membership of the
elliptic measure associated with $L$ to the class $A_\infty$ yields that the
domain is indeed a chord-arc domain.
