Vertaisarvioitu alkuperäisartikkeli tai data-artikkeli tieteellisessä aikakauslehdessä (A1)

Level sets of potential functions bisecting unbounded quadrilaterals

Julkaisun tekijätNasser Mohamed M.S, Nasyrov Semen, Vuorinen Matti



JournalAnalysis and Mathematical Physics

Tietokannassa oleva lehden nimiANALYSIS AND MATHEMATICAL PHYSICS

Lehden akronyymiANAL MATH PHYS


Sivujen määrä15





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(oo) 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.

Last updated on 2022-28-11 at 08:47