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

Andrzej Stos (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

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

Mots clés: Stable processes; Sierpinski carpet; harmonic functions; boundary Harnack principle

Domaines: Probabilités [math.PR]

Andrzej Stos. Boundary Harnack Principle for fractional powers of Laplacian on the Sierpinski carpet. Bull. Sci. Math., 2006, 130 (2006), no. 7, pp.580--594. ⟨hal-00004492⟩