The Laplacian on the Sierpinski gasket via the method of averages

Robert S. Strichartz

Vol. 201 (2001), No. 1, 241–257

DOI: 10.2140/pjm.2001.201.241

Abstract

We show how the symmetric Laplacian on the Sierpinski gasket, together with its associated Dirichlet form and harmonic functions, can be defined entirely in terms of average values of a function over basic sets. This approach combines the constructive limit–of–difference–quotients method of Kigami and the method of averages introduced by Kusuoka and Zhou for the Sierpinski carpet.

Milestones

Received: 9 July 1999

Revised: 5 January 2000

Published: 1 November 2001