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Nonlocal operators related to nonsymmetric forms I: H\"older estimates

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arxiv 2203.07418 v1 pith:MFPWRS7P submitted 2022-03-14 math.AP math.PR

Moritz Kassmann , Marvin Weidner This is my paper · ORCID
classification math.APmath.PR
keywords operatorsnonlocalnonsymmetricformsolderregularityresultstheory
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The aim of this article is to develop the regularity theory for parabolic equations driven by nonlocal operators associated with nonsymmetric forms. H\"older regularity and weak Harnack inequalities are proved using extensions of recently established nonlocal energy methods. We are able to connect the theory of nonsymmetric nonlocal operators with the important results of Aronson-Serrin in the local linear case. This connection is exemplified by nonlocal-to-local convergence results identifying the limiting class of operators as second order differential operators with drift terms.

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Cited by 2 Pith papers

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  1. 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.

  2. 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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