Gradient estimates for a parabolic 𝑝-Laplace equation with logarithmic nonlinearity on Riemannian manifolds

Wang, Yu-Zhao; Xue, Yan

doi:10.1090/proc/15275

Gradient estimates for a parabolic $p$-Laplace equation with logarithmic nonlinearity on Riemannian manifolds
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by Yu-Zhao Wang and Yan Xue PDF

Proc. Amer. Math. Soc. 149 (2021), 1329-1341 Request permission

Abstract:

In this paper, we study gradient estimates for a parabolic $p$-Laplace equation with logarithmic nonlinearity, which is related to the $L^p$-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 $p$-Laplace equation with logarithmic nonlinearity on compact Riemannian manifolds with nonnegative Ricci curvature. As applications, the corresponding Harnack inequalities are derived.

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