Sharp sub-Gaussian upper bounds for subsolutions of Trudinger's equation on Riemannian manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910333333929984 |
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| author | Sürig, Philipp |
| author_facet | Sürig, Philipp |
| contents | We consider on Riemannian manifolds the nonlinear evolution equation \begin{equation*} \partial _{t}u=Δ_{p}(u^{1/(p-1)}), \end{equation*}% where $p>1$. This equation is also known as a doubly non-linear parabolic equation or Trudinger's equation. We prove that weak subsolutions of this equation have a sub-Gaussian upper bound and prove that this upper bound is sharp for a specific class of manifolds including $\mathbb{R}^{n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01218 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sharp sub-Gaussian upper bounds for subsolutions of Trudinger's equation on Riemannian manifolds Sürig, Philipp Analysis of PDEs Differential Geometry We consider on Riemannian manifolds the nonlinear evolution equation \begin{equation*} \partial _{t}u=Δ_{p}(u^{1/(p-1)}), \end{equation*}% where $p>1$. This equation is also known as a doubly non-linear parabolic equation or Trudinger's equation. We prove that weak subsolutions of this equation have a sub-Gaussian upper bound and prove that this upper bound is sharp for a specific class of manifolds including $\mathbb{R}^{n}$. |
| title | Sharp sub-Gaussian upper bounds for subsolutions of Trudinger's equation on Riemannian manifolds |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2309.01218 |