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arXiv · 2107.13846

A matrix Harnack inequality for semilinear heat equations

Giacomo Ascione·Daniele Castorina·Giovanni Catino·Carlo Mantegazza
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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 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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Giacomo Ascione, Daniele Castorina, Giovanni Catino, Carlo Mantegazza. 2021-07-29. A matrix Harnack inequality for semilinear heat equations. https://arxiv.org/abs/2107.13846

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