Carleson measure estimates for the Green function
Analysis of PDEs
2021-12-22 v2
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.
Cite
@article{arxiv.2102.09592,
title = {Carleson measure estimates for the Green function},
author = {Guy David and Linhan Li and Svitlana Mayboroda},
journal= {arXiv preprint arXiv:2102.09592},
year = {2021}
}
Comments
39 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