Gradient Estimate for Solutions of the Equation ∆pu = a|∇u|q +becu 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 (unauthenticated)
  • 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, <i>p</i>-Laplace

Abstract

In this paper, a universal gradient estimate for a quasilinear elliptic equation ∆pu = a|∇u|q + becu on 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

Issue

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

Section

Research Article

Categories

License

Copyright (c) 2025 Hui Yang, et al.

Creative Commons License

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

How to Cite

1.
Gradient Estimate for Solutions of the Equation ∆pu = a|∇u|q +becu on a Complete Riemannian Manifold. Contemp. Math. [Internet]. 2025 Jun. 4 [cited 2025 Dec. 24];6(3):3433-5. Available from: https://ojs353.mebyme.cn/index.php/CM/article/view/6649