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arXiv · 2603.27791

Sharp long distance upper bounds for solutions of Leibenson's equation on Riemannian manifolds

Alexander Grigor'yan·Jin Sun·Philipp Sürig
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Abstract

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}.

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Alexander Grigor'yan, Jin Sun, Philipp Sürig. 2026-03-29. Sharp long distance upper bounds for solutions of Leibenson's equation on Riemannian manifolds. https://arxiv.org/abs/2603.27791

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