Title page for E-project-083109-173751

Project Type MQP

Submission date 2009-08-31

Author
Eric Mbakop, MA

URN E-project-083109-173751

Title Analysis 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

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Project Type	MQP
Submission date	2009-08-31
Author	Eric Mbakop, MA
URN	E-project-083109-173751
Title	Analysis 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