Second-Order Gradient Estimates for the Porous Medium Equation on Riemannian Manifolds

Jingjing Yang and Guangwen Zhao ()
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Jingjing Yang: School of Mathematics and Statistics, Wuhan University of Technology, Wuhan 430070, China
Guangwen Zhao: School of Mathematics and Statistics, Wuhan University of Technology, Wuhan 430070, China

Mathematics, 2025, vol. 13, issue 10, 1-14

Abstract: In this paper, we derive second-order gradient estimates for positive solutions of the porous medium equation ∂ ∂ t u ( x , t ) = Δ u ( x , t ) p , p ∈ 1 , 1 + 1 n − 1 on an n -dimensional Riemannian manifold under certain curvature conditions.

Keywords: gradient estimate; porous medium equation; Riemannian manifold (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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