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 by catino on 04 Mar 2023


Published Paper

Inserted: 10 jan 2022
Last Updated: 4 mar 2023

Journal: Ann. Mat. Pura Appl.
Volume: 202
Pages: 827-850
Year: 2023


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.