Level sets of potential functions bisecting unbounded quadrilaterals
| Autor: | Nasser, Mohamed M. S., Nasyrov, Semen, Vuorinen, Matti |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 14 pages, 5 figures |
| Databáze: | arXiv |
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