Gradient estimates and entropy formulae of porous medium and fast diffusion equations for the Witten Laplacian
Gradient estimates and entropy formulae of porous medium and fast diffusion equations for the Witten Laplacian
We study gradient estimates for the positive solutions of the porous medium equations and the fast diffusion equationsassociated with the Witten Laplacian on Riemannian manifolds.Under the assumption that the m-dimensional Bakry-Emery Ricci curvature is bounded from below, we obtain some gradient estimates which generalize some previous results of Lu et.al. …