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Hölder regularity for the fractional p-Laplacian, revisited

  • Filippo Maria Cassanello , Fatma Gamze Düzgün and Antonio Iannizzotto ORCID logo EMAIL logo
Published/Copyright: March 28, 2025

Abstract

We present an alternative proof for local Hölder regularity of the solutions of the fractional p-Laplace equations, based on clustering and expansion (more precisely, recentering) of positivity.

MSC 2020: 35R11; 35B65

Communicated by Ugo Gianazza


Funding statement: The authors are members of GNAMPA (Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica ’Francesco Severi’). Antonio Iannizzotto is partially supported by the research project Problemi non locali di tipo stazionario ed evolutivo (GNAMPA, CUP E53C23001670001).

Acknowledgements

We would like to thank the anonymous Referees for their useful comments.

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Received: 2024-10-01
Accepted: 2025-02-11
Published Online: 2025-03-28
Published in Print: 2025-07-01

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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