WG4 Research Seminar - Talk by Rico Zacher

On March 21st, 2022, Prof. Dr. Rico Zacher (University Ulm) will give a talk at 3:30 pm CET about

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

The talk will be held online in Zoom as part of the research seminar Analysis of the FernUniversität in Hagen. The zoom URL will be sent to all members of the WG4 and to all further colleagues who send a mail to Delio Mugnolo.

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 to the fractional (in space). 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).