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In the summer 2002, a group of REU students have worked on a research project under the direction of Professor Robert Strichartz of Cornell University Mathematics Department. REU stands for "Research Experiences for Undergraduates Program". My group studied properties of functions defined on the familiar Sierpinski gasket (also called the Sierpinski triangle) and there is now a theory of "differential equation" on it. Most of the work on this project will involve both computer experimentation and theoretical study, but individual students may put more emphasis on one or the other.

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BACKGROUND

A stage for defining a p-Laplacian on the Sierpinski gasket (abbreviated by SG throughout this website)  is already set up by the students last year.

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OBJECTIVES

  1. Try to solve the solution of u = f  with given boundary values numerically (by transforming it into a minimization problem), where f  is a given function.

  2. Figure out the pointwise formula of u, which is useful in both practical and theoretical purpose.

  3. Understand the local behavior of p-harmonic functions.

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If you have any question or comment, send mail to: Carto Wong.