Gradient estimates for weighted $p$-Laplacian equations on Riemannian manifolds with a Sobolev inequality and integral Ricci bounds

Le Van Dai, Nguyen Thac Dung, Nguyen Dang Tuyen +1

In this paper, we consider the non-linear general $p$-Laplacian equation ${\Delta }_{p,f}u+F(u)=0$ for a smooth function $F$ on smooth metric measure spaces. Assume that a Sobolev inequali…