dc.contributor.author Nasser, Mohamed M.S. dc.contributor.author Nasyrov, Semen dc.contributor.author Vuorinen, Matti dc.date.accessioned 2022-11-28T21:14:50Z dc.date.available 2022-11-28T21:14:50Z dc.date.issued 2022-11-10 dc.identifier.citation Nasser, M.M.S., Nasyrov, S. & Vuorinen, M. Level sets of potential functions bisecting unbounded quadrilaterals. Anal.Math.Phys. 12, 149 (2022). https://doi.org/10.1007/s13324-022-00732-3 dc.identifier.issn 1664-2368 dc.identifier.uri https://doi.org/10.1007/s13324-022-00732-3 dc.identifier.uri https://soar.wichita.edu/handle/10057/24232 dc.description Preprint version available from arXiv. Click on the DOI to access the publisher's version of this article. dc.description.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 potential function of the quadrilateral. We compute the values of the potential function u including its value at infinity. The main result of this paper is Theorem 4.3 which yields a formula for u(?) expressed in terms of the angles of the polygonal given quadrilateral and the well-known special functions. We use two independent numerical methods to illustrate our result. The first method is a Mathematica program and the second one is based on using the MATLAB toolbox PlgCirMap. The case of a quadrilateral, which is the exterior of the unit disc with four fixed points on its boundary, is considered as well. dc.language.iso en_US dc.publisher Birkhauser dc.relation.ispartofseries Analysis and Mathematical Physics dc.relation.ispartofseries 2022 dc.subject Quadrilateral dc.subject Hyperbolic geometry dc.subject Conformal mapping dc.subject Schwarz–Christoffel formula dc.subject Dirichlet–Neumann boundary value problem dc.subject Potential function dc.title Level sets of potential functions bisecting unbounded quadrilaterals dc.type Preprint dc.rights.holder © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022
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