Gradient estimates for Leibenson's equation on Riemannian manifolds
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913884986671104 |
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| author | Sürig, Philipp |
| author_facet | Sürig, Philipp |
| contents | We consider on Riemannian manifolds solutions of the Leibenson equation \begin{equation*} \partial _{t}u=Δ_{p}u^{q}. \end{equation*} This equation is also known as doubly nonlinear evolution equation. We prove gradient estimates for positive solutions $u$ under the condition that the Ricci curvature on $M$ is bounded from below by a non-positive constant. We distinguish between the case $q(p-1)>1$ (slow diffusion case) and the case $q(p-1)<1$ (fast diffusion case). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07221 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gradient estimates for Leibenson's equation on Riemannian manifolds Sürig, Philipp Analysis of PDEs 35K55, 58J35, 53C21, 35B05 We consider on Riemannian manifolds solutions of the Leibenson equation \begin{equation*} \partial _{t}u=Δ_{p}u^{q}. \end{equation*} This equation is also known as doubly nonlinear evolution equation. We prove gradient estimates for positive solutions $u$ under the condition that the Ricci curvature on $M$ is bounded from below by a non-positive constant. We distinguish between the case $q(p-1)>1$ (slow diffusion case) and the case $q(p-1)<1$ (fast diffusion case). |
| title | Gradient estimates for Leibenson's equation on Riemannian manifolds |
| topic | Analysis of PDEs 35K55, 58J35, 53C21, 35B05 |
| url | https://arxiv.org/abs/2506.07221 |