Gradient estimates for a class of quasilinear elliptic equations on manifolds
Abstract
In this paper, we mainly investigate some local and global properties of positive solutions to the degenerate elliptic equation Δp u + a∇ u^p + b u^q e^c u= 0 defined on a Riemannian manifold. We establish Cheng-Yau type gradient estimates for positive solutions of this equation. As corollaries, we derive Harnack inequalities and Liouville theorems for such solutions.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Geometric Analysis and Curvature Flows
Advanced Differential Geometry Research
Publication details
- Journal / source
- Scientia Sinica Mathematica
- Publication date
- 1 February 2026
- Language
- EN