Green function for a hyperbolic strip and a class of related plane domains

Abstract

The parqueting reflection principle serves to construct the harmonic Green function for a hyperbolic strip in the unit disc. The formula obtained represents the Green functions also for the set of strips covering the unit disc and related to the original strip by continued reflection at the boundaries. A complementary unbounded domain is also included. The complex plane is covered by the closures of countably many domains having all the same expression for their Green functions.

Keywords:

• Green function
• Dirichlet problem
• Poisson equation
• hyperbolic strip
• parqueting reflection principle

AMS Subject Classifications:

• 31A25
• 30E25
• 35J05
• 35J08
• 35J25
• 35C15

Notes

Dedicated to Professor LinWei on the occasion of his 80th birthday.