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, Δu+(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
Support for NREUP is provided by the National Science Foundation Division of Mathematical Sciences, the National Security Agency and The Moody's Foundation.