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AuthorNasser, Mohamed M.S.
AuthorNasyrov, Semen
AuthorVuorinen, Matti
Available date2024-03-12T08:43:18Z
Publication Date2022-12
Publication NameAnalysis and Mathematical Physics
Identifierhttp://dx.doi.org/10.1007/s13324-022-00732-3
CitationNasser, M. M., Nasyrov, S., & Vuorinen, M. (2022). Level sets of potential functions bisecting unbounded quadrilaterals. Analysis and Mathematical Physics, 12(6), 149.
ISSN1664-2368
URIhttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85141841064&origin=inward
URIhttp://hdl.handle.net/10576/52943
AbstractWe 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.
SponsorVolga Region Mathematical Center (agreement no. 075-02-2022-882).
Languageen
PublisherSpringer Nature
SubjectConformal mapping
Dirichlet–Neumann boundary value problem
Hyperbolic geometry
Potential function
Quadrilateral
Schwarz–Christoffel formula
TitleLevel sets of potential functions bisecting unbounded quadrilaterals
TypeArticle
Issue Number6
Volume Number12
ESSN1664-235X
dc.accessType Full Text


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