Boundary Harnack inequality for α-harmonic functions on the Sierpiński triangle

  1. Kamil Kaleta
  2. Mateusz Kwaśnicki

Abstract

We prove a uniform boundary Harnack inequality for nonnegative functions harmonic with respect to _-stable process on the Sierpiński triangle, where α ∈ (0, 1). Our result requires no regularity assumptions on the domain of harmonicity.
2000 AMS Mathematics Subject Classification: Primary: 60J45.

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Probability and Mathematical Statistics

30, z. 2, 2010

Pages from 353 to 368

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