Einladung zum Vortrag (Zoom) von Herrn Prof. Dr. Rico Zacher am 21.03.2022 - 15:30 Uhr im Rahmen des Forschungsseminars Analysis


Im Rahmen des Forschungsseminars Analysis hält am Montag, den 21. März 2022, um 15:30 Uhr,

Herr Prof. Dr. Rico Zacher (Universität Ulm)

einen Vortrag zum Thema

Li-Yau inequalities for general non-local diffusion equations via reduction to the heat kernel

Abstract: I will present a reduction principle to derive Li-Yau inequalities for non-local diffusion problems in a very general framework, which covers both the discrete and continuous setting. The approach is not based on curvature-dimension inequalities but on heat kernel representations of the solutions and consists in reducing the problem to the heat kernel. As an important application we obtain a Li-Yau inequality for positive solutions $u$ to the fractional (in space) heat equation of the form $(-\Delta)^{\beta/2}(\log u)\le C/t$, where $\beta\in (0,2)$. I will also show that this Li-Yau inequality allows to derive a Harnack inequality. The general result is further illustrated with an example in the discrete setting by proving a sharp Li-Yau inequality for diffusion on a complete graph.

This is joint work with Frederic Weber (Münster).

Der Vortrag findet im Rahmen eines Zoom-Meetings statt. Bei Interesse an den Zugangsdaten bitte bei Herrn Prof. Mugnolo (delio.mugnolo@fernuni-hagen.de) melden.

mathinf.webteam | 14.03.2022