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 -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.