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

Guy David, Linhan Li, Svitlana Mayboroda

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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.

Original languageEnglish (US)
Article number109553
JournalJournal of Functional Analysis
Issue number5
StatePublished - 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.


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


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