Poisson Integral Formulas in Generalized Bi-Axially Symmetric Potential Theory

Abstract

Poisson integral formulas are given which solve certain Dirichlet problems for a “quarter-ball” for the equation of generalized bi-axially symmetric potential theory. The formulas are useful in studying properties of solutions of this equation and related equations. The equation considered includes the equation of Weinstein's generalized axially symmetric potential theory for which corresponding Poisson integral formulas were given by A. Huber.