Gradient estimate for the Poisson equation and the non-homogeneous heat equation on compact Riemannian manifolds

2009/07/09 by Li Ma, Liang Cheng, Ma, Li +1
Mathematics · #35J60 #53C21 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.AP #math.DG #msc:35J60 #msc:53C21

paper · pdf · doi:10.48550/arxiv.0907.1440

6 pages

arxiv created 2009/07/09 · openalex publication_date 2009/07/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short note, we study the gradient estimate of positive solutions to Poisson equation and the non-homogeneous heat equation in a compact Riemannian manifold (Mⁿ,g). Our results extend the gradient estimate for positive harmonic functions and positive solutions to heat equations.

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