### 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.

: Primary 35J60; secondary 35B53.

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 Wednesday, January 31, 2018