Gradient estimates for a class of p-Laplace equations on Riemannian manifolds

By virtue of the Nash-Moser iteration, we obtain local gradient estimates of positive weak solutions to the weighted p -Laplace equation ( p − 1 ) p − 1 Δ p , f u + a u p − 1 ln ⁡ u p − 1 = 0 defined on a complete smooth metric measure space under the condition that the m -Bakry-Émery Ricci curvature has a lower bound, where p > 2 and a is a negative constant. As applications, Liouville type theorems for solutions to the above equation are achieved.