Semilinear Li & Yau inequalities
Daniele Castorina, Giovanni Catino, Carlo Mantegazza
TL;DR
This paper extends Li & Yau inequalities to semilinear heat equations on Riemannian manifolds, providing new estimates and applications such as Harnack inequalities and analysis of ancient solutions.
Contribution
It introduces adapted Li & Yau estimates for semilinear heat equations on manifolds with nonnegative Ricci curvature, advancing the understanding of their solutions.
Findings
Derived new Li & Yau type estimates for semilinear heat equations
Established Harnack inequalities for these solutions
Analyzed properties of ancient and eternal solutions
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Point processes and geometric inequalities