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

## TL;DR

This paper develops explicit harmonic Green and Neumann functions for domains bounded by two intersecting circular arcs with a specific angle, enabling solutions to boundary value problems in these geometries.

## Contribution

It extends the parqueting-reflection principle to construct harmonic functions in domains with intersecting circular arcs, providing explicit formulas for boundary value problems.

## Key findings

- Explicit Green functions derived for domains with intersecting circular arcs.
- Solutions to Dirichlet and Neumann problems obtained using Green and Neumann functions.
- Application of reflection principle to complex domain geometries.

## 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 $\pi/n, n\in\mathbb{N}^*$. 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.