Carleson perturbations of locally Lipschitz elliptic operators

In 1-sided chord-arc domains Ω \Omega , we demonstrate that the A ∞ A_\infty -absolute continuity of the elliptic measure with respect to the surface measure remains stable under L 2 L^2 Carleson perturbations. This stability holds provided that either the elliptic operator L 0 = − d i v A 0 ∇ L_0=-divA_0\nabla , which is being perturbed, or the perturbed operator L 1 = − d i v A 1 ∇ L_1=-divA_1\nabla satisfies the condition sup X ∈ Ω d i s t ( X , ∂ Ω ) | ∇ A i ( X ) | > ∞ \sup _{X\in \Omega }dist(X,\partial \Omega )|\nabla A_i(X)| >\infty on its coefficients. L 2 L^2 Carleson perturbations are slightly more general than those previously discussed in the literature. The proof hinges on the availability of a comprehensive elliptic theory and a domain Ω \Omega that allows uniform non-tangential access to any point on its boundary. Consequently, while the current theory of