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| Main Author: | |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1902.11013 |
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| _version_ | 1866916205897449472 |
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| author | Zhao, Guangwen |
| author_facet | Zhao, Guangwen |
| contents | In this paper, we consider a manifold evolving by a general geometric flow and study parabolic equation \[ (Δ-q(x,t)-\partial_t)u(x,t)=A(u(x,t)),\quad (x,t)\in M\times [0,T]. \] We establish space-time gradient estimates for positive solutions and elliptic type gradient estimates for bounded positive solutions of this equation. By integrating the gradient estimates, we derive the corresponding Harnack inequalities. Finally, as applications, we give gradient estimates of some specific parabolic equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1902_11013 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Gradient estimates and Harnack inequalities of a parabolic equation under geometric flow Zhao, Guangwen Differential Geometry In this paper, we consider a manifold evolving by a general geometric flow and study parabolic equation \[ (Δ-q(x,t)-\partial_t)u(x,t)=A(u(x,t)),\quad (x,t)\in M\times [0,T]. \] We establish space-time gradient estimates for positive solutions and elliptic type gradient estimates for bounded positive solutions of this equation. By integrating the gradient estimates, we derive the corresponding Harnack inequalities. Finally, as applications, we give gradient estimates of some specific parabolic equations. |
| title | Gradient estimates and Harnack inequalities of a parabolic equation under geometric flow |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/1902.11013 |