Universal gradient estimates for solutions of $\Delta_{p,f}u+au^{\sigma}\ln u=0$ on complete Riemannian manifolds

Jingxu Liu; Zhen Wang

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arXiv · 2604.06605

Universal gradient estimates for solutions of $\Delta_{p,f}u+au^{\sigma}\ln u=0$ on complete Riemannian manifolds

Jingxu Liu·Zhen Wang

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Abstract

In this paper, we consider the weighted $p$-Laplacian equation $$ \Delta_{p,f}u+au^{\sigma}\ln u=0$$ defined on a complete smooth metric measure space under the conditon that the $m$-Bakry-\'{E}mery Ricci curvature has a lower bound, where $a$, $\sigma$ are two nonzero real constants. By applying the Nash-Moser iteration, we obtain sharp gradient estimates and thereby establish Liouville theorems for the above equation.

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BibTeX RIS

Jingxu Liu, Zhen Wang. 2026-04-08. Universal gradient estimates for solutions of $\Delta_{p,f}u+au^{\sigma}\ln u=0$ on complete Riemannian manifolds. https://arxiv.org/abs/2604.06605

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