Calculus of Variations and Geometric Measure Theory

G. Ascione - D. Castorina - G. Catino - C. Mantegazza

A matrix Harnack inequality for semilinear heat equations

created by catino on 29 Jul 2021
modified by mantegaz on 05 May 2022


Published Paper

Inserted: 29 jul 2021
Last Updated: 5 may 2022

Journal: Math. Engineering
Volume: 5
Number: 1
Pages: Paper n.003, 15 pp.
Year: 2023


We derive a matrix version of Li & Yau-type estimates for positive solutions of semilinear heat equations on Riemannian manifolds with nonnegative sectional curvatures and parallel Ricci tensor, similarly to what R. Hamilton did for the standard heat equation. We then apply these estimates to obtain some Harnack-type inequalities, which give local bounds on the solutions in terms of the geometric quantities involved.