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arXiv · 2309.01218

Sharp sub-Gaussian upper bounds for subsolutions of Trudinger's equation on Riemannian manifolds

Philipp Sürig
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Abstract

We consider on Riemannian manifolds the nonlinear evolution equation \begin{equation*} \partial _{t}u=\Delta _{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 $\mathbb{R}^{n}$.

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Philipp Sürig. 2023-09-03. Sharp sub-Gaussian upper bounds for subsolutions of Trudinger's equation on Riemannian manifolds. https://arxiv.org/abs/2309.01218

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