Numerical computation of Stephenson's g-functions in multiply connected domains
Green, Christopher C. Nasser, Mohamed M. S.
Green, Christopher C.
Nasser, Mohamed M. S.
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2026-02-15
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Article
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Boundary integral equation,Conforman mapping,g-Function,Generalized Neumann kernel,Multiply connected domain
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Green, C. C., & Nasser, M. M. S. (2026). Numerical computation of Stephenson's g-functions in multiply connected domains. Journal of Mathematical Analysis and Applications, 554(2). https://doi.org/10.1016/j.jmaa.2025.130010
Abstract
There has been much recent attention on h-functions, so named since they describe the distribution of harmonic measure for a given multiply connected domain with respect to some basepoint. In this paper, we focus on a closely related function to the h-function, known as the g-function, which originally stemmed from questions posed by Stephenson in [3]. Computing the values of the g-function for a given planar domain and some basepoint in this domain requires solving a Dirichlet boundary value problem whose domain and boundary condition change depending on the input argument of the g-function. We use a well-established boundary integral equation method to solve the relevant Dirichlet boundary value problems and plot various graphs of the g-functions for different multiply connected circular and rectilinear slit domains.
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Elsevier
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Journal of Mathematical Analysis and Applications
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0022247X
10960813
10960813