Gradient estimates for the 𝑝-Laplacian Lichnerowicz equation on smooth metric measure spaces

Zhao, Liang; Yang, Dengyun

doi:10.1090/proc/13997

Gradient estimates for the $p$-Laplacian Lichnerowicz equation on smooth metric measure spaces
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by Liang Zhao and Dengyun Yang PDF

Proc. Amer. Math. Soc. 146 (2018), 5451-5461 Request permission

Abstract:

In this paper, we consider the weighted $p$-Laplacian Lichnerowicz equation \begin{equation*} \triangle _{p,f} u+cu^{\sigma }=0 \end{equation*} on smooth metric measure spaces, where $c\geq 0, p>1,$ and $\sigma \leq p-1$ are real constants. A local gradient estimate for positive solutions to this equation is derived, and as applications, we give a corresponding Liouville property and Harnack inequality.

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