Calculus of Variations and Geometric Measure Theory

D. Castorina - G. Catino - C. Mantegazza

Semilinear Li & Yau inequalities

created by root on 10 Jan 2022
modified on 25 Sep 2022


Accepted Paper

Inserted: 10 jan 2022
Last Updated: 25 sep 2022

Journal: Ann. Mat. Pura Appl.
Year: 2022


We derive an adaptation of Li & Yau estimates for positive solutions of semilinear heat equations on Riemannian manifolds with nonnegative Ricci tensor. We then apply these estimates to obtain a Harnack inequality and to discuss monotonicity, convexity, decay estimates and triviality of ancient and eternal solutions.