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H\"older regularity for fractional $p$-Laplace equations

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arxiv 2203.13082 v2 pith:IO5Z435A submitted 2022-03-24 math.AP

Karthik Adimurthi , Harsh Prasad , Vivek Tewary This is my paper · ORCID
classification math.AP
keywords equationsfractionaliterationnonlocalolderregularityalternativeballs
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We give an alternative proof for H\"older regularity for weak solutions of nonlocal elliptic quasilinear equations modelled on the fractional p-Laplacian where we replace the discrete De Giorgi iteration on a sequence of concentric balls by a continuous iteration. This work can be viewed as the nonlocal counterpart to the ideas developed by Tiziano Granucci.

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  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.

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