Aronson-Bénilan gradient estimates for porous medium equations under lower bounds of N-weighted Ricci curvature with N < 0

2023/01/18 by Yasuaki Fujitani, Fujitani, Yasuaki · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2301.07622

openalex publication_date 2023/01/18 · openalex created_date 2023/01/20 · openalex updated_date 2026/07/28

Abstract

The Aronson-Bénilan gradient estimate for the porous medium equation has been studied as a counterpart to the Li-Yau gradient estimate for the heat equation. In this paper, we give the Aronson-Bénilan gradient estimates for the porous medium equation on weighted Riemannian manifolds under lower bounds of N-weighted Ricci curvature with ε-range for some N &lt; 0. This is a generalization of those estimates under constant lower N-weighted Ricci curvature bounds with N∈ [n,∞).

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