Gradient estimates and Liouville type theorems for Poisson equations

Nguyen Thac Dung, Nguyen Ngoc Khanh

In this paper, we will address to the following parabolic equation $$u_t={\Delta }_{f}u+F(u)$$ on a smooth metric measure space with Bakry-Émery curvature bounded from below. Here $F$ is…