Higher differentiability for the fractional $p$-Laplacian
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909230338932736 |
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| author | Diening, Lars Kim, Kyeongbae Lee, Ho-Sik Nowak, Simon |
| author_facet | Diening, Lars Kim, Kyeongbae Lee, Ho-Sik Nowak, Simon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16727 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher differentiability for the fractional $p$-Laplacian Diening, Lars Kim, Kyeongbae Lee, Ho-Sik Nowak, Simon Analysis of PDEs 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. |
| title | Higher differentiability for the fractional $p$-Laplacian |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.16727 |