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

摘要

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, 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. (c) 2022 Elsevier Inc. All rights reserved.