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Hölder regularity for fractional \({\varvec{p}}\)-Laplace equations

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Abstract

We give an alternative proof for Hölder 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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Authors and Affiliations

  1. Tata Institute of Fundamental Research, Centre for Applicable Mathematics, Bengaluru, 560 065, India

    Karthik Adimurthi & Harsh Prasad

  2. School of Interwoven Arts and Sciences, Krea University, Sri City, 517 646, India

    Vivek Tewary

Authors
  1. Karthik Adimurthi
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  2. Harsh Prasad
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  3. Vivek Tewary
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Correspondence to Vivek Tewary.

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Communicating Editor: K Sandeep.

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Adimurthi, K., Prasad, H. & Tewary, V. Hölder regularity for fractional \({\varvec{p}}\)-Laplace equations. Proc Math Sci 133, 14 (2023). https://doi.org/10.1007/s12044-023-00734-6

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  • DOI: https://doi.org/10.1007/s12044-023-00734-6

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