  In the present paper, we consider an elliptic divergence form operator in the
half-space and prove that its Green function is almost affine, or more
precisely, that the normalized difference between the Green function and a
suitable affine function at every scale satisfies a Carleson measure estimate,
provided that the oscillations of the coefficients satisfy the traditional
quadratic Carleson condition. The results are sharp, and in particular, it is
demonstrated that the class of the operators considered in the paper cannot be
improved.
