Gradient estimates for nonlinear elliptic equations with a gradient-dependent nonlinearity

Joshua Ching and Florica C. Cîrstea

Abstract

In this paper, we obtain gradient estimates of the positive solutions to weighted \(p\)-Laplacian type equations with a gradient-dependent nonlinearity without any upper bound restriction on the power of the gradient. Our proof of the gradient estimates is based on a two-step process relying on a modified version of the Bernstein's method. As a by-product, we extend the range of applicability of the Liouville-type results known for our problem.

Keywords: Liouville-type result, isolated singularities, quasilinear elliptic equation.

AMS Subject Classification: Primary 35J60; secondary 35B53.