Carleson perturbations of locally Lipschitz elliptic operators

In 1-sided Chord Arc Domains Ω, we show that the A_∞-absolute continuity of the elliptic measure is stable under L² Carleson perturbations provided that the elliptic operator L₀=- div A₀∇ which is being perturbed satisfies \[X∈ Ω{ dist}(X,∂ Ω)|∇ A_0(X)| <∞.\] L² Carleson perturbations are are more natural and slightly more general than the Carleson perturbations previously found in the literature (those would be "L^∞ Carleson perturbations"). We decided to limit the article to 1-sided CAD to make it more accessible, but the proof can easily extended to more general setting as long as we have a rich elliptic theory and the domain is 1-sided NTA.