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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 parabolicequation or Trudinger's equation. We prove that weak subsolutions of thisequation have a sub-Gaussian upper bound and prove that this upper bound issharp for a specific class of manifolds including $\mathbb{R}^{n}$.

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