Gradient estimates for some evolution equations on complete smooth\n metric measure spaces

2016/10/11 by Nguyen Thac Dung, Dung, Nguyen Thac, Kieu Thi Thuy Linh +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Primary 32M05 #Secondary 32H02

paper · pdf · doi:10.48550/arxiv.1610.03198

openalex publication_date 2016/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the following general evolution equation ν_t=
Delta_fu+au
log^
alpha u+bu on smooth metric measure spaces (Mⁿ, g,≠^-fdv). We give a local gradient estimate of Souplet-Zhang type for\npositive smooth solution of this equation provided that the Bakry- 'Emery\ncurvature bounded from below. When f is constant, we investigate the gereral\nevolution on compact Riemannian manifolds with no nconvex boundary satisfying\nan "\interior rolling R-ball" condition. We show a gradient estimate of\nHamilton type on such manifolds.\n

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