Carleson measure estimates for the Green function

Abstract

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.

arXiv comment39 pages. Added a remark on the estimates for the second derivatives of the Green function. Added the definition of the Green function with pole at infinity. To appear in Arch. Ration. Mech. Anal

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• Carleson measure estimates for the Green function
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Cited by in corpus (3)

• Carleson measure estimates for the Green function
• The Green function with pole at infinity applied to the study of the elliptic measure
• A Green function characterization of uniformly rectifiable sets of any codimension