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 |
|---|---|
| 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 |
