Calculus of Variations and Geometric Measure Theory
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G. Ascione - D. Castorina - G. Catino - C. Mantegazza

A matrix Harnack inequality for semilinear heat equations

created by catino on 29 Jul 2021


Submitted Paper

Inserted: 29 jul 2021
Last Updated: 29 jul 2021

Year: 2021


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 in~\cite{hamilton7} 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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