A non-linear characterization of stochastic completeness of graphs
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914724796432384 |
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| author | Schmidt, Marcel Zimmermann, Ian |
| author_facet | Schmidt, Marcel Zimmermann, Ian |
| contents | We study non-linear Schrödinger operators on graphs. We construct minimal nonnegative solutions to corresponding semi-linear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a non-linear setting. We provide characterizations for this property in terms of a semi-linear Liouville theorem. It is employed to establish a non-linear characterization for stochastic completeness, which is a graph version of a recent result on Riemannian manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15125 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A non-linear characterization of stochastic completeness of graphs Schmidt, Marcel Zimmermann, Ian Analysis of PDEs Functional Analysis Metric Geometry We study non-linear Schrödinger operators on graphs. We construct minimal nonnegative solutions to corresponding semi-linear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a non-linear setting. We provide characterizations for this property in terms of a semi-linear Liouville theorem. It is employed to establish a non-linear characterization for stochastic completeness, which is a graph version of a recent result on Riemannian manifolds. |
| title | A non-linear characterization of stochastic completeness of graphs |
| topic | Analysis of PDEs Functional Analysis Metric Geometry |
| url | https://arxiv.org/abs/2403.15125 |