Li-Yau and Harnack estimates for nonlocal diffusion problems
Rico Zacher
TL;DR
This paper introduces differential Harnack inequalities and summarizes key results on Li-Yau and Harnack estimates specifically for nonlocal diffusion problems, highlighting recent advances in PDE analysis.
Contribution
It provides a concise overview of recent developments in Li-Yau and Harnack estimates tailored to nonlocal diffusion equations, emphasizing new inequalities and their applications.
Findings
Summarizes main results on nonlocal diffusion Harnack inequalities
Highlights recent progress in Li-Yau estimates for PDEs
Provides insights into oscillation phenomena in PDEs
Abstract
These notes give a brief introduction to differential Harnack inequalities and summarise the main results of the mini-course ``Li-Yau and Harnack estimates for nonlocal diffusion problems'', presented by the author at the Seasonal School on PDEs ``Oscillation Phenomena, PDEs, and Applications: A Comprehensive School in Mathematical Analysis'', held at Ghent University in October 2025.
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