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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2501.12685 |
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| _version_ | 1866912199307427840 |
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| author | Camilli, Fabio |
| author_facet | Camilli, Fabio |
| contents | We prove a Li-Yau gradient estimate for positive solutions to the heat equation defined on a metric star graph $\mG$ given by the heat kernel formula. As consequence, we derive a Harnack estimate and a Liouville property for bounded harmonic functions. The argument exploits an explicit representation formula for the heat kernel on $\mG$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12685 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Li-Yau inequality and related properties on metric star graphs Camilli, Fabio Analysis of PDEs 35R02, 35A23, 58J35 We prove a Li-Yau gradient estimate for positive solutions to the heat equation defined on a metric star graph $\mG$ given by the heat kernel formula. As consequence, we derive a Harnack estimate and a Liouville property for bounded harmonic functions. The argument exploits an explicit representation formula for the heat kernel on $\mG$. |
| title | Li-Yau inequality and related properties on metric star graphs |
| topic | Analysis of PDEs 35R02, 35A23, 58J35 |
| url | https://arxiv.org/abs/2501.12685 |