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- W4287549002 abstract "We establish 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. Our 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 solve a long-standing open problem by obtaining a Li-Yau inequality for positive solutions $u$ to the fractional (in space) heat equation of the form $(-Delta)^{beta/2}(log u)leq C/t$, where $betain (0,2)$. We also illustrate our general result with an example in the discrete setting by proving a sharp Li-Yau inequality for diffusion on a complete graph." @default.
- W4287549002 created "2022-07-25" @default.
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- W4287549002 date "2020-12-23" @default.
- W4287549002 modified "2023-09-25" @default.
- W4287549002 title "Li-Yau inequalities for general non-local diffusion equations via reduction to the heat kernel" @default.
- W4287549002 doi "https://doi.org/10.48550/arxiv.2012.12974" @default.
- W4287549002 hasPublicationYear "2020" @default.
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