Backward Harnack inequality and Hamilton estimates for heat type equations
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918131322060800 |
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| author | Lu, Juanling Wu, Yuting Zhang, Qi S. |
| author_facet | Lu, Juanling Wu, Yuting Zhang, Qi S. |
| contents | Based on gradient estimates for the heat equation by Hamilton, we discover a backward in time Harnack inequality for positive solutions on compact manifolds without further restrictions such as boundedness or vanishing boundary value for solutions. Contrary to the usual Harnack inequality, it allows comparison of the values of a solution at two different space time points, in both directions of time. In view of the importance of the usual Harnack inequality, further application is expected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19680 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Backward Harnack inequality and Hamilton estimates for heat type equations Lu, Juanling Wu, Yuting Zhang, Qi S. Analysis of PDEs Differential Geometry 53C55, 58J05 Based on gradient estimates for the heat equation by Hamilton, we discover a backward in time Harnack inequality for positive solutions on compact manifolds without further restrictions such as boundedness or vanishing boundary value for solutions. Contrary to the usual Harnack inequality, it allows comparison of the values of a solution at two different space time points, in both directions of time. In view of the importance of the usual Harnack inequality, further application is expected. |
| title | Backward Harnack inequality and Hamilton estimates for heat type equations |
| topic | Analysis of PDEs Differential Geometry 53C55, 58J05 |
| url | https://arxiv.org/abs/2508.19680 |