Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.04629 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916924297838592 |
|---|---|
| author | Green, Christopher C. Nasser, Mohamed M S |
| author_facet | Green, Christopher C. Nasser, Mohamed M S |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04629 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical computation of Stephenson's g-functions in multiply connected domains Green, Christopher C. Nasser, Mohamed M S Complex Variables 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. |
| title | Numerical computation of Stephenson's g-functions in multiply connected domains |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2504.04629 |