A Li-Yau gradient estimate for the Finslerian logarithmic Schrödinger equation
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914021423185920 |
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| author | Zhao, Zisu |
| author_facet | Zhao, Zisu |
| contents | By leveraging a new Laplacian comparison theorem, we derive a Li-Yau type gradient estimate for a particular nonlinear parabolic equation, namely, the Finslerian logarithmic Schrodinger equation on a non-compact, complete Finsler manifold with mixed weighted Ricci curvature bounded from below. In our framework, all coefficients are time-dependent functions defined on the manifold. As applications, we establish both a Harnack inequality and an a priori estimate for the positive solutions of this specific equation |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06237 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Li-Yau gradient estimate for the Finslerian logarithmic Schrödinger equation Zhao, Zisu Differential Geometry Analysis of PDEs 53A45 By leveraging a new Laplacian comparison theorem, we derive a Li-Yau type gradient estimate for a particular nonlinear parabolic equation, namely, the Finslerian logarithmic Schrodinger equation on a non-compact, complete Finsler manifold with mixed weighted Ricci curvature bounded from below. In our framework, all coefficients are time-dependent functions defined on the manifold. As applications, we establish both a Harnack inequality and an a priori estimate for the positive solutions of this specific equation |
| title | A Li-Yau gradient estimate for the Finslerian logarithmic Schrödinger equation |
| topic | Differential Geometry Analysis of PDEs 53A45 |
| url | https://arxiv.org/abs/2507.06237 |