New differential Harnack inequalities for nonlinear heat equations

2018/03/28 by Jia-Yong Wu, Wu, Jia-Yong · 1 citation
Mathematics · Physics and Astronomy · #53C44 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1803.10622

openalex publication_date 2018/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove constrained trace, matrix and constrained matrix Harnack inequalities for the nonlinear heat equation ω_t=Δω+aωln ω on closed manifolds. We also derive a new interpolated Harnack inequality for the equation ω_t=Δω-ωlnω+ε Rω on closed surfaces under the ε-Ricci flow. Finally we prove a new differential Harnack inequality for the equation ω_t=Δω-ωlnω under the Ricci flow without any curvature condition. Among these Harnack inequalities, the correction terms are all time-exponential functions, which are superior to time-polynomial functions.

Citations

• On the parabolic kernel of the Schrödinger operator
• Logarithmic Sobolev Inequalities

Cited by

• Matrix Li-Yau-Hamilton Estimates for Nonlinear Heat Equations

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