Student Work

Analysis on Fractals

Public

Downloadable Content

open in viewer

In this paper we study the standard Dirichlet form and its associated energy measures and Laplacians on the Sierpinski gasket, and Related fractals constructed by Kigami. We first obtain a pointwise formula for the Kusuoka Laplacian, and then the intersection of its domain and that of the standard Laplacian is shown to be the set of harmonic functions. The standard measure is then shown to be the only one with respect to which the harmonic functions satisfy a certain type of mean value property.

  • This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.
Creator
Publisher
Identifier
  • E-project-083109-173751
Advisor
Year
  • 2009
Date created
  • 2009-08-31
Resource type
Major
Rights statement

Relations

In Collection:

Items

Items

Permanent link to this page: https://digital.wpi.edu/show/np193b858