Worcester Polytechnic Institute Electronic Projects Collection

Title page for E-project-083109-173751

Project TypeMQP
Submission date2009-08-31
Author
  • Eric Mbakop, steve055@WPI.EDU, MA
    • URNE-project-083109-173751
    TitleAnalysis on Fractals
    Advisor
  • Vernescu, Bogdan M., MA
    • Availability unrestricted

    Abstract

    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.

    Files
  • MathMQP.pdf

    There is one file which has been withheld at the advisor's request.

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