Long time upper bounds for solutions of Leibenson's equation on Riemannian manifolds

Philipp Sürig

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arXiv · 2604.23227

Long time upper bounds for solutions of Leibenson's equation on Riemannian manifolds

Philipp Sürig

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Abstract

We consider on Riemannian manifolds the Leibenson equation $$\partial _{t}u=\Delta _{p}u^{q}.$$ We prove that a certain upper bound for weak solutions of this equation is equivalent to a euclidean-type Sobolev inequality.

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Philipp Sürig. 2026-04-25. Long time upper bounds for solutions of Leibenson's equation on Riemannian manifolds. https://arxiv.org/abs/2604.23227

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