Level sets of potential functions bisecting unbounded quadrilaterals
Complex Variables
2022-06-06 v1
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 and 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.
Cite
@article{arxiv.2206.01316,
title = {Level sets of potential functions bisecting unbounded quadrilaterals},
author = {Mohamed M. S. Nasser and Semen Nasyrov and Matti Vuorinen},
journal= {arXiv preprint arXiv:2206.01316},
year = {2022}
}
Comments
14 pages, 5 figures