On Li–Yau Heat Kernel Estimate

We present some improvements of the Li–Yau heat kernel estimate on a Riemannian manifold with Ricci curvature bounded below. As a consequence we prove a gradient estimate to the heat kernel with an optimal leading term.     

Li-Yau Harnack Estimates for a Heat-Type Equation Under the Geometric Flow

Potential Analysis - In this paper, we consider the gradient estimates for a postive solution of the nonlinear parabolic equation ?tu = Δtu + hup on a Riemannian manifold whose metrics...     

Li-Yau type estimates for a nonlinear parabolic equation on complete manifolds

Let (M,g) be a complete noncompact Riemannian manifold with the m-dimensional Bakry-Émery Ricci curvature bounded below. In this paper, we give a local Li-Yau type gradient estimate for the positive solutions to a general nonlinear parabolic equation

ut=Δu−∇?⋅∇u−aulogu−qu     

Li-Yau Inequality for Heat Equations on RCD∗(K,N) Metric Measure Spaces

Potential Analysis - In this paper, we will study the Li-Yau inequalities for weak solutions of the heat equation on RCD?(K,N) metric measure spaces.