| File | |
| Title |
1-harmonic functions on a network
|
| Creator |
Kurata Hisayasu
Yamasaki Maretsugu
|
| Source Title |
島根大学総合理工学研究科紀要. シリーズB
|
| Volume | 48 |
| Start Page | 1 |
| End Page | 14 |
| Journal Identifire |
ISSN 13427121
|
| Descriptions |
Abstract
A minimizer of the Dirichlet norm of order 1 is called a 1-harmonic function. The aim of this paper is a research of properties of 1-harmonic functions on a network. First we consider the 1-Dirichlet space and show that every network is of 1-hyperbolic type and that the ideal boundary coincides with the 1-harmonic boundary. Next we introduce the notion of 1-harmonic functions and that of strongly 1-harmonic functions. We discuss the Dirichlet problem and the maximum principle with respect to (strongly) 1-harmonic functions.
|
| Subjects |
discrete potential theory
1-harmonic function
strongly 1-harmonic function
|
| Language |
eng
|
| Resource Type | departmental bulletin paper |
| Publisher |
島根大学総合理工学研究科
|
| Date of Issued | 2015-03 |
| Publish Type | Version of Record |
| Access Rights | open access |
| Relation |
[NCID]
AA12638295
|
