Published Paper

Inserted: 29 jul 2021
Last Updated: 7 jul 2025

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

Abstract:

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.

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• Semilinear_Matrix_Harnack.pdf