Harmonic Green and Neumann functions for domains bounded by two intersecting circular arcs

Abstract

The parqueting-reflection principle is shown to also work for constructing harmonic Green functions and harmonic Neumann functions for a class of domains, which are bounded by two arcs in $\mathbb{C}$ with a special intersecting angle $\pi /n,n\in {\mathbb{N}}^{\ast }$. Applying the Green representation formula and the Neumann representation formula we solve the Dirichlet and Neumann boundary problem to the Poisson equation in these domains.

17 pages, 2 figures