Abstract
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 language | English (US) |
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Article number | 107687 |
Journal | Advances in Mathematics |
Volume | 383 |
DOIs | |
State | Published - Jun 4 2021 |
Bibliographical note
Publisher Copyright:© 2021 Elsevier Inc.
Keywords
- Cantor set
- Counterexample
- Elliptic operator
- Green function
- Harmonic measure