Regularity for the fractional p-Laplace equation
Higher Sobolev and Hölder regularity is studied for local weak solutions of the fractional p -Laplace equation of order s in the case p ≥ 2 . Depending on the regime considered, i.e. 0 < s ≤ p − 2 p or p − 2 p < s < 1 , precise local estimates are proven. The relevant estimates are stable if the fractional order s reaches 1; the known Sobolev regularity estimates for the local p -Laplace are recovered. The case p = 2 reproduces the almost W loc 1 + s , 2 -regularity for the fractional Laplace equation of any order s ∈ ( 0 , 1 ) .
Authors
- Verena Bögelein (ORCID: https://orcid.org/0000-0002-5646-2023)
- Giovanni Molica Bisci (ORCID: https://orcid.org/0000-0003-4802-1727)
- Naian Liao (ORCID: https://orcid.org/0000-0003-2378-148X)
- Frank Duzaar (ORCID: https://orcid.org/0000-0002-6643-1634)
- Raffaella Servadei (ORCID: https://orcid.org/0000-0002-0636-6463)
Institutions
- University of Salzburg (AT)
- University of Urbino (IT)
Publication Details
- Journal
- Journal of Functional Analysis
- Published
- 2025-05-30
- DOI
- https://doi.org/10.1016/j.jfa.2025.111078
- Citations
- 6
- Primary Topic
- Nonlinear Partial Differential Equations
- Type
- article
- Field-Weighted Citation Impact
- 22.36
Funders
- European Commission
- Austrian Science Fund
- Ministero dell’Istruzione, dell’Università e della Ricerca
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni