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Harnack estimates for nonlocal drift-diffusion equations

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arxiv 2402.11986 v2 pith:442PW25U submitted 2024-02-19 math.AP

Naian Liao This is my paper · ORCID
classification math.AP
keywords estimatesequationsharnacknonlocalapproachaspectscasecertain
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A set of pointwise estimates are established for local solutions to nonlocal diffusion equations with a drift term. In particular, our Harnack estimates are the first ones for such equations, and our H\"older regularity refines certain known result in several aspects. The approach is measure theoretical in the spirit of DeGiorgi classes. It yields novel nonlocal weak Harnack estimates in the elliptic case as well.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Nonnegative solutions to nonlocal parabolic equations

    math.AP 2025-05 conditional novelty 8.0 of 10

    Nonnegative solutions to nonlocal parabolic equations with bounded measurable coefficients are represented exactly by a fundamental solution, with sharp two-sided bounds and new Harnack inequalities.

  2. Harnack estimates for the nonlocal Trudinger equation

    math.AP 2026-07 conditional novelty 6.0 of 10

    Weak solutions of the nonlocal Trudinger equation obey a quantitative sup-bound with optimal tail and a time-gapped strong Harnack inequality.

  3. Nonlocal parabolic De Giorgi classes

    math.AP 2025-08 unverdicted novelty 6.0 of 10

    Pure-measure-theory De Giorgi-type estimates yield local boundedness, weak Harnack, Harnack, Hölder, and Liouville results for nonlocal parabolic energy classes, with a comparison-principle-free Harnack proof.

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