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We consider on Riemannian manifolds the Leibenson equation \begin{equation*}\partial _{t}u=\Delta _{p}(u^{1/(p-1)}), \end{equation*} where $p>1$. Thisequation is also known as a doubly nonlinear evolution equation. We prove thatweak subsolutions to this equation have a Gaussian upper bound.

Gaussian upper bounds for subsolutions of Leibenson's equation on Riemannian manifolds