Abstract
A generalization of Robin boundary conditions leading to self-adjoint operators is developed for the second derivative operator
on metric graphs with compact completion and totally disconnected boundary. Harmonic functions and
their properties play an essential role.
Для оператора другої похідної розроблено узагальнення
граничних умов Робена, що веде до самоспряжених операторів на
метричних графах з компактним поповненням і повністю незв'язною
границею. Істотну роль відіграють гармонічні функції і їх
властивості.
Key words: Quantum graph, harmonic functions on graphs, boundary value problems.
Full Text
Article Information
| Title | Robin boundary conditions for the Laplacian on metric graph completions |
| Source | Methods Funct. Anal. Topology, Vol. 28 (2022), no. 1, 12-24 |
| MathSciNet |
MR4459180 |
| Milestones | Received 09/12/2021; Revised 24/03/2022 |
| Copyright | The Author(s) 2022 (CC BY-SA) |
Authors Information
Robert Carlson
Department of Mathematics, University of Colorado at Colorado Springs, Colorado Springs, CO 80918 USA
Citation Example
Robert Carlson, Robin boundary conditions for the Laplacian on metric graph completions, Methods Funct. Anal. Topology 28
(2022), no. 1, 12-24.
BibTex
@article {MFAT1722,
AUTHOR = {Robert Carlson},
TITLE = {Robin boundary conditions for the Laplacian on metric graph completions},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {28},
YEAR = {2022},
NUMBER = {1},
PAGES = {12-24},
ISSN = {1029-3531},
MRNUMBER = {MR4459180},
URL = {http://mfat.imath.kiev.ua/article/?id=1722},
}
