Sharp long distance upper bounds for solutions of Leibenson's equation on Riemannian manifolds
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912987582824448 |
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| author | Grigor'yan, Alexander Sun, Jin Sürig, Philipp |
| author_facet | Grigor'yan, Alexander Sun, Jin Sürig, Philipp |
| contents | We consider on Riemannian manifolds the Leibenson equation $\partial _{t}u=Δ_{p}u^{q}$ that is also known as a doubly nonlinear evolution equation. We prove sharp upper estimates of weak subsolutions to this equation on Riemannian manifolds with non-negative Ricci curvature in the whole range of $p>1$ and $q>0$ satisfying $q(p-1)<1$. In this way, we improve the result of \cite{Grigoryan2024a} and prove Conjecture 1.2 from \cite{Grigoryan2024a}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27791 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp long distance upper bounds for solutions of Leibenson's equation on Riemannian manifolds Grigor'yan, Alexander Sun, Jin Sürig, Philipp Analysis of PDEs Differential Geometry 35K55, 58J35, 35B05 We consider on Riemannian manifolds the Leibenson equation $\partial _{t}u=Δ_{p}u^{q}$ that is also known as a doubly nonlinear evolution equation. We prove sharp upper estimates of weak subsolutions to this equation on Riemannian manifolds with non-negative Ricci curvature in the whole range of $p>1$ and $q>0$ satisfying $q(p-1)<1$. In this way, we improve the result of \cite{Grigoryan2024a} and prove Conjecture 1.2 from \cite{Grigoryan2024a}. |
| title | Sharp long distance upper bounds for solutions of Leibenson's equation on Riemannian manifolds |
| topic | Analysis of PDEs Differential Geometry 35K55, 58J35, 35B05 |
| url | https://arxiv.org/abs/2603.27791 |