Uniform rectifiability and elliptic operators satisfying a Carleson measure condition (Q2041864)

For an optimal class of divergence form elliptic operators satisfying some conditions, the authors prove the equivalence of the absolute continuity of the elliptic measure with respect to the surface measure and the uniform rectifiability of the boundary of a domain under the Dahlberg-Kenig-Pipher condition on the coefficients. They investigate two cases for the coefficients, and in the proof of the main results they use geometric measure theory and an extrapolation argument.