Universal gradient estimates for solutions of ${\Delta }_{p,f}u+a{u}^{\sigma }\ln u=0$ on complete Riemannian manifolds

Jingxu Liu, Zhen Wang

In this paper, we consider the weighted $p$-Laplacian equation $${\Delta }_{p,f}u+a{u}^{\sigma }\ln u=0$$ defined on a complete smooth metric measure space under the conditon that the $m$-Bakry-Éme…