Higher differentiability for the fractional p-Laplacian

Diening L, Kim K, Lee H-S, Nowak SN (2025)
Mathematische Annalen 391: 5631–5693.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
In this work, we study the higher differentiability of solutions to the inhomogeneous fractional $p$-Laplace equation under different regularity assumptions on the data. In the superquadratic case, we extend and sharpen several previous results, while in the subquadratic regime our results constitute completely novel developments even in the homogeneous case. In particular, in the local limit our results are consistent with well-known higher differentiability results for the standard inhomogeneous $p$-Laplace equation. All of our main results remain valid in the vectorial context of fractional $p$-Laplace systems.
Erscheinungsjahr
2025
Zeitschriftentitel
Mathematische Annalen
Band
391
Seite(n)
5631–5693
Page URI
https://pub.uni-bielefeld.de/record/2990865

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Diening L, Kim K, Lee H-S, Nowak SN. Higher differentiability for the fractional p-Laplacian. Mathematische Annalen. 2025;391:5631–5693.
Diening, L., Kim, K., Lee, H. - S., & Nowak, S. N. (2025). Higher differentiability for the fractional p-Laplacian. Mathematische Annalen, 391, 5631–5693. https://doi.org/10.1007/s00208-024-03057-7
Diening, Lars, Kim, Kyeongbae, Lee, Ho-Sik, and Nowak, Simon Noah. 2025. “Higher differentiability for the fractional p-Laplacian”. Mathematische Annalen 391: 5631–5693.
Diening, L., Kim, K., Lee, H. - S., and Nowak, S. N. (2025). Higher differentiability for the fractional p-Laplacian. Mathematische Annalen 391, 5631–5693.
Diening, L., et al., 2025. Higher differentiability for the fractional p-Laplacian. Mathematische Annalen, 391, p 5631–5693.
L. Diening, et al., “Higher differentiability for the fractional p-Laplacian”, Mathematische Annalen, vol. 391, 2025, pp. 5631–5693.
Diening, L., Kim, K., Lee, H.-S., Nowak, S.N.: Higher differentiability for the fractional p-Laplacian. Mathematische Annalen. 391, 5631–5693 (2025).
Diening, Lars, Kim, Kyeongbae, Lee, Ho-Sik, and Nowak, Simon Noah. “Higher differentiability for the fractional p-Laplacian”. Mathematische Annalen 391 (2025): 5631–5693.
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arXiv: 2406.16727

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