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Gradient estimates for a parabolic 𝑝-Laplace equation with logarithmic nonlinearity on Riemannian manifolds
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2021-01-25 , DOI: 10.1090/proc/15275 Yu-Zhao Wang , Yan Xue
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2021-01-25 , DOI: 10.1090/proc/15275 Yu-Zhao Wang , Yan Xue
Abstract:In this paper, we study gradient estimates for a parabolic 
-Laplace equation with logarithmic nonlinearity, which is related to the 
-log-Sobolev constant on Riemannian manifolds. We prove a global Li-Yau type gradient estimate and a Hamilton type gradient estimate for positive solutions to a parabolic 
-Laplace equation with logarithmic nonlinearity on compact Riemannian manifolds with nonnegative Ricci curvature. As applications, the corresponding Harnack inequalities are derived.
中文翻译：
黎曼流形上具有对数非线性的抛物线𝑝-Laplace方程的梯度估计
摘要：本文研究具有对数非线性的抛物线-Laplace方程的梯度估计，该方程与黎曼流形上的-log-Sobolev常数有关。我们证明了在具有非负Ricci曲率的紧黎曼流形上具有对数非线性的抛物线-Laplace方程正解的全局Li-Yau型梯度估计和Hamilton型梯度估计。作为应用，得出相应的Harnack不等式。
更新日期：2021-02-08
-Laplace equation with logarithmic nonlinearity, which is related to the -log-Sobolev constant on Riemannian manifolds. We prove a global Li-Yau type gradient estimate and a Hamilton type gradient estimate for positive solutions to a parabolic -Laplace equation with logarithmic nonlinearity on compact Riemannian manifolds with nonnegative Ricci curvature. As applications, the corresponding Harnack inequalities are derived. 中文翻译：
黎曼流形上具有对数非线性的抛物线𝑝-Laplace方程的梯度估计
摘要：本文研究
具有对数非线性的抛物线-Laplace方程的梯度估计，该方程与黎曼流形上的-log-Sobolev常数有关。我们证明了在具有非负Ricci曲率的紧黎曼流形上具有对数非线性的抛物线-Laplace方程正解的全局Li-Yau型梯度估计和Hamilton型梯度估计。作为应用，得出相应的Harnack不等式。
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