Harmonic Functions in Flat-Ring Coordinates

Lijuan Bi
University of Wisconsin-Milwaukee
PhD Graduate Student

“We will derive expansions for afundamental solution of the Laplace’s equation in flat-ring coordinates in three-dimensional Euclidean space. These expansions are in terms of harmonic  functions in two different types of regions, “flat rings” and “peanuts”. The internal and external “flat-ring” and “peanut”  harmonic functions are expressed in terms of Lamé functions, respectively.”

Committee Members:
Profs. Hans Volkmer (Advisor); Peter Hinow, Gabriella Pinter, Dexuan Xie & Jeb Willenbring