Boundary Harnack Principle for fractional powers of Laplacian on the Sierpinski carpet

2005/03/16 by Andrzej Stos, Andrzej Stós, Stos, Andrzej
Computer Science · Mathematics · #60J35 #60J45 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #advanced mathematical theories #math.PR #msc:60J35 #msc:60J45

paper · pdf · doi:10.48550/arxiv.math/0503333

arxiv created 2005/03/16 · openalex publication_date 2005/03/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the Boundary Harnack Principle related to fractional powers of Laplacian for some natural regions in the two-dimensional Sierpinski carpet. This is a natual application of a probabilistic method based on the Ikeda-Watanabe formula

Citations

• Brownian Motion and Harmonic Analysis on Sierpinski Carpets

Related

• Boundary Harnack inequalities for regional fractional Laplacian
• On the Boundary Harnack Principle in Holder domains
• The Boundary Harnack Principle and the 3G Principle in Fractal-Type Spaces
• Brownian Motion and Harmonic Analysis on Sierpinski Carpets
• Boundary Harnack principle for Δ+ Δ^α/2