Gradient estimates for the porous medium type equations and fast diffusion type equations on complete noncompact metric measure space with compact boundary
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866914913036795904 |
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| author | Cao, Xiangzhi |
| author_facet | Cao, Xiangzhi |
| contents | In the paper, we derive Li-Yau gradient estimates and Souplet Zhang type estimates of the following equation \begin{equation*} \begin{split} u_t= Δ_ξp+λu+A(u) , \end{split} \end{equation*} on complete noncompact metric measure space $ (M, g,e^{-ξ}dv_g) $ with compact boundary. We will also give the local gradient estimates of the equation \begin{equation*} Δ_ξ(u^p)+λu+A(u)=0, \end{equation*} on complete noncompact manifold with compact boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_00224 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Gradient estimates for the porous medium type equations and fast diffusion type equations on complete noncompact metric measure space with compact boundary Cao, Xiangzhi Differential Geometry Analysis of PDEs 58E15, 58E20, 53C27 In the paper, we derive Li-Yau gradient estimates and Souplet Zhang type estimates of the following equation \begin{equation*} \begin{split} u_t= Δ_ξp+λu+A(u) , \end{split} \end{equation*} on complete noncompact metric measure space $ (M, g,e^{-ξ}dv_g) $ with compact boundary. We will also give the local gradient estimates of the equation \begin{equation*} Δ_ξ(u^p)+λu+A(u)=0, \end{equation*} on complete noncompact manifold with compact boundary. |
| title | Gradient estimates for the porous medium type equations and fast diffusion type equations on complete noncompact metric measure space with compact boundary |
| topic | Differential Geometry Analysis of PDEs 58E15, 58E20, 53C27 |
| url | https://arxiv.org/abs/2210.00224 |