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arXiv · 2107.08101

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

Guy David·Linhan Li·Svitlana Mayboroda
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Abstract

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.

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Guy David, Linhan Li, Svitlana Mayboroda. 2021-07-16. Carleson estimates for the Green function on domains with lower dimensional boundaries. https://arxiv.org/abs/2107.08101

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