Gradient Estimates for the doubly nonlinear diffusion equation on Complete Riemannian Manifolds
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908313684279296 |
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| author | Guo, Chen Zhang, Zhengce |
| author_facet | Guo, Chen Zhang, Zhengce |
| contents | We study the elliptic version of doubly nonlinear diffusion equations on a complete Riemannian manifold $(M,g)$. Through the combination of a special nonlinear transformation and the standard Nash-Moser iteration procedure, some Cheng-Yau type gradient estimates for positive solutions are derived. As by-products, we also obtain Liouville type results and Harnack's inequality. These results fill a gap in Yan and Wang (2018)\cite{YW}, due to the lack of one key inequality when $b=γ-\frac{1}{p-1}>0$, and provide a partial answer to the question that whether gradient estimates for the doubly nonlinear diffusion equation can be extended to the case $b>0$ . |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08276 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gradient Estimates for the doubly nonlinear diffusion equation on Complete Riemannian Manifolds Guo, Chen Zhang, Zhengce Analysis of PDEs We study the elliptic version of doubly nonlinear diffusion equations on a complete Riemannian manifold $(M,g)$. Through the combination of a special nonlinear transformation and the standard Nash-Moser iteration procedure, some Cheng-Yau type gradient estimates for positive solutions are derived. As by-products, we also obtain Liouville type results and Harnack's inequality. These results fill a gap in Yan and Wang (2018)\cite{YW}, due to the lack of one key inequality when $b=γ-\frac{1}{p-1}>0$, and provide a partial answer to the question that whether gradient estimates for the doubly nonlinear diffusion equation can be extended to the case $b>0$ . |
| title | Gradient Estimates for the doubly nonlinear diffusion equation on Complete Riemannian Manifolds |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.08276 |