Good elliptic operators on Cantor sets

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It is well known that a purely unrectifiable set cannot support a harmonic measure which is absolutely continuous with respect to the Hausdorff measure of this set. We show that nonetheless there exist elliptic operators on (purely unrectifiable) Cantor sets in R2 whose elliptic measure is absolutely continuous, and in fact, essentially proportional to the Hausdorff measure.

Original languageEnglish (US)
Article number107687
JournalAdvances in Mathematics
StatePublished - Jun 4 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Inc.


  • Cantor set
  • Counterexample
  • Elliptic operator
  • Green function
  • Harmonic measure


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