SMALL A_∞ RESULTS FOR DAHLBERG-KENIG-PIPHER OPERATORS IN SETS WITH UNIFORMLY RECTIFIABLE BOUNDARIES

In the present paper we consider elliptic operators L = − div(A∇) in a domain bounded by a chord-arc surface Γ with small enough constant, and whose coefficients A satisfy a weak form of the Dahlberg-Kenig-Pipher condition of approximation by constant coefficient matrices, with a small enough Carleson norm, and show that the elliptic measure with pole at infinity associated to L is A∞-absolutely continuous with respect to the surface measure on Γ, with a small A∞ constant. In other words, we show that for relatively flat uniformly rectifiable sets and for operators with slowly oscillating coefficients the elliptic measure satisfies the A∞ condition with a small constant and the logarithm of the Poisson kernel has small oscillations.