Gradient Estimate for Solutions of the Equation ∆pu = a|∇u|q +becu on a Complete Riemannian Manifold

Jie He; Yilu Liu; Shiyun Wen; Hui Yang

doi:10.37256/cm.6320256649

Gradient Estimate for Solutions of the Equation ∆_pu = a|∇u|^q +be^cu on a Complete Riemannian Manifold

Authors

Jie He School of Mathematics and Physics, Beijing University of Chemical Technology, Beijing, 100029, China https://orcid.org/0000-0003-4454-1784
Yilu Liu Department of Mathematics, University of Science and Technology of China, Hefei, 230026, China
Shiyun Wen Department of Informatics, Beijing City University, Beijing, 101309, China
Hui Yang School of Mathematics, Yunnan Normal University, Kunming, 650500, China

DOI:

https://doi.org/10.37256/cm.6320256649

Keywords:

non-linear elliptic equation, gradient estimate, p-Laplace

Abstract

In this paper, a universal gradient estimate for a quasilinear elliptic equation ∆_pu = a|∇u|^q+ be^cuon a Riemannian manifold is presented. As applications, a Liouville theorem and Harnack inequalities for positive solutions are established. These results cover gradient estimates for many equations, including the quasi-linear Hamilton-Jacobi equation, the Lane-Emden equation, and others.

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Published

2025-06-04

How to Cite

He J, Liu Y, Wen S, Yang H. Gradient Estimate for Solutions of the Equation ∆pu = a|∇u|q +becu on a Complete Riemannian Manifold. Contemp. Math. [Internet]. 2025 Jun. 4 [cited 2026 Jun. 4];6(3):3433-5. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/6649

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Issue

Contemporary Mathematics, Volume 6 Issue 3 (2025), 2726-3845

Section

Research Article

License

This work is licensed under a Creative Commons Attribution 4.0 International License.