English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We establish a reduction principle to derive Li-Yau inequalities fornon-local diffusion problems in a very general framework, which covers both thediscrete and continuous setting. Our approach is not based oncurvature-dimension inequalities but on heat kernel representations of thesolutions and consists in reducing the problem to the heat kernel. As animportant application we solve a long-standing open problem by obtaining aLi-Yau inequality for positive solutions $u$ to the fractional (in space) heatequation of the form $(-\Delta)^{\beta/2}(\log u)\leq C/t$, where $\beta\in(0,2)$. We also illustrate our general result with an example in the discretesetting by proving a sharp Li-Yau inequality for diffusion on a complete graph.

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