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Cody Holdaway |
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Mentor: Elena Cherkaev Majors: Mathematics & Physics Summer 2007 project description: The goal of this project is to study the Laplacian on the Sierpinski Gasket. Jun Kigami defined the Laplacian as the limit of difference operators on the gaskets G(sub m) whose limit is the Sierpinski Gasket. An algorithm for the Dirichlet eigenfunctions has been developed and I hope to do a similar development for the Neumann eigenfunctions and study some of the properties of these eigenfunctions. Also I would like to extend the results to other Laplacian like operators on the SG by similar methods or possibly by the minimization of energy functionals and try to solve some differential equations on the Sierpinski Gasket. Spring 2008 project description: This project will be a continuation of an REU done during the summer of 2007 in which I studied the Laplacian operator on the Sierpinski gasket. Originally, the Laplacian was defined as the limit of difference operators on the pre-gaskets which approximate the Sierpinski gasket. There is a more general definition using a measure on the Sierpinski gasket to get a Laplacian type operator and using this definition with different measures gives a different Laplacian operator. The goal of this REU will be to study laplacian operators on the Sierpinski gasket in this more general setting and look at some common differential equations on the gasket. |
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