Carleson estimates for the Green function on domains with lower dimensional boundaries

In the present paper we consider an elliptic divergence form operator in Rn∖Rd with d<n−1 and prove that its Green function is almost affine, sense normalized difference between a sufficiently far away pole suitable affine at every scale satisfies Carleson measure estimate. The coefficients of can be very oscillatory, only need to satisfy some condition similar traditional quadratic condition.