Gradient Estimate for Solutions of the Equation ∆pu = a|∇u|q +becu on a Complete Riemannian Manifold (Contemporary Mathematics, 2025)
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.
Keywords: non-linear elliptic equation; gradient estimate; p-Laplace