A note on Neumann problems on graphs
- We discuss Neumann problems for self-adjoint Laplacians on (possibly infinite) graphs. Under the assumption that the heat semigroup is ultracontractive we discuss the unique solvability for non-empty subgraphs with respect to the vertex boundary and provide analytic and probabilistic representations for Neumann solutions. A second result deals with Neumann problems on canonically compactifiable graphs with respect to the Royden boundary and provides conditions for unique solvability and analytic and probabilistic representations.
Author details: | Michael HinzORCiDGND, Michael SchwarzGND |
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DOI: | https://doi.org/10.1007/s11117-022-00930-0 |
ISSN: | 1385-1292 |
ISSN: | 1572-9281 |
Title of parent work (English): | Positivity |
Publisher: | Springer |
Place of publishing: | Dordrecht |
Publication type: | Article |
Language: | English |
Date of first publication: | 2022/07/26 |
Publication year: | 2022 |
Release date: | 2023/12/08 |
Tag: | Discrete Dirichlet forms; Graphs; Neumann problem; Royden boundary |
Volume: | 26 |
Issue: | 4 |
Article number: | 68 |
Number of pages: | 23 |
Funding institution: | Projekt DEAL |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access / Hybrid Open-Access |
License (German): | CC-BY - Namensnennung 4.0 International |