Carleson Measure Estimates for the Green Function

Guy David, Linhan Li, Svitlana Mayboroda

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1525-1563
Number of pages39
JournalArchive For Rational Mechanics And Analysis
Volume243
Issue number3
DOIs
StatePublished - Mar 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 the Simons foundation Grant 563916, SM.

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature.

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