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