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arXiv · 1904.04316

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

Hanxing Lin
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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.

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Hanxing Lin. 2019-04-08. Harmonic Green and Neumann functions for domains bounded by two intersecting circular arcs. https://doi.org/10.1080/17476933.2020.1816984

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