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arXiv · 2206.01316

Level sets of potential functions bisecting unbounded quadrilaterals

Mohamed M. S. Nasser·Semen Nasyrov·Matti Vuorinen
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Abstract

We study the mixed Dirichlet-Neumann problem for the Laplace equation in the complement of a bounded convex polygonal quadrilateral in the extended complex plane. The Dirichlet\,/\,Neumann conditions at opposite pairs of sides are $\{0,1\}$ and $\{0,0\},$ resp. The solution to this problem is a harmonic function in the unbounded complement of the polygon known as the \emph{potential function} of the quadrilateral. We compute the values of the potential function including its value at infinity.

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Mohamed M. S. Nasser, Semen Nasyrov, Matti Vuorinen. 2022-06-02. Level sets of potential functions bisecting unbounded quadrilaterals. https://arxiv.org/abs/2206.01316

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