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

Guy David; Linhan Li; Svitlana Mayboroda

doi:10.1016/j.jfa.2022.109553

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

Guy David, Linhan Li, Svitlana Mayboroda

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In the present paper we consider an elliptic divergence form operator in Rⁿ∖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.

Original language	English (US)
Article number	109553
Journal	Journal of Functional Analysis
Volume	283
Issue number	5
DOIs	https://doi.org/10.1016/j.jfa.2022.109553
State	Published - Sep 1 2022

Bibliographical note

Funding Information:
G. David was partially supported by the European Community H2020 grant GHAIA 777822 , and the Simons Foundation grant 601941 , GD. S. Mayboroda was partly supported by the NSF RAISE-TAQS grant DMS-1839077 and Simons Foundation grant 563916 , SM.

Publisher Copyright:
© 2022 Elsevier Inc.

Keywords

Carleson measures
Lower-dimensional boundaries
The Green function
Variable coefficient elliptic operators

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

Abstract

Bibliographical note

Keywords

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