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NREUP 2008

Virginia Union University

Title: Harmonic Functions and related Differential Equations

Director: Dawit W. Aberra

Email: dwaberra@vuu.edu

Dates of Program: May 19 - June 27, 2008

Summary: The simplest elliptic differential equation with constant coefficients is the Laplace equation. The axially symmetric PDE, Î?u+(k/y)uy=0, where k is a constant and u=u(x,y), may be considered as the simplest among those with variable coefficients. For general parameter k, the study of such class is referred as Generalized Axially Symmetric Potential Theory (GASPT). Investigation and generalization of properties that are known to hold for harmonic functions in R2 to the class of generalized axially symmetric potentials is classical yet not exhausted. We will generalize some simple properties of harmonic functions in R2 to this class of GASPs. A particular emphasis will be given to generalizing the reflection principle for harmonic functions in R2 to this class of potentials with simple assumptions on the reflecting curve and the parameter k.

Student Researchers Supported by MAA:

  • Eugene Webb Evans
  • Emanuel Sekyere
  • Ciara Alston

Program Contacts:

Bill Hawkins
MAA SUMMA
bhawkins@maa.org
202-319-8473

Michael Pearson
MAA Programs & Services
pearson@maa.org
202-319-8470

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