A new differential Harnack inequality for nonlinear equations

We prove a sharp nonlinear version of the celebrated Li-Yau inequality for positive solutions of the normalized (so called "game-theoretic") parabolic p-Laplacian equation. We obtain the inequality with sharp constant on closed manifolds with non-negative Ricci curvature. Additionally, similar to the original result of Li and Yau for Laplacian, we obtain the inequality with a relaxed constant on closed manifolds and (under an additional growth assumption) on complete manifolds with Ricci curvature bounded from below. This is joint work with Nicola Garofalo and Agnid Banerjee.