Sobolev regularity for the nonlocal $(1, p)$-Laplace equations in the superquadratic case
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915312475045888 |
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| author | Li, Dingding Zhang, Chao |
| author_facet | Li, Dingding Zhang, Chao |
| contents | We investigate the interior Sobolev regularity of weak solutions to the nonlocal $(1, p)$-Laplace equations in the superquadratic case $p\ge 2$. As a product, the explicit Hölder continuity estimates of weak solutions are derived. The proof relies on a detailed analysis of the structural characteristics of $(1, p)$-growth in the nonlocal setting, combined with the finite difference quotient method, tail estimates, refined energy estimates, and a Moser-type iteration scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23288 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sobolev regularity for the nonlocal $(1, p)$-Laplace equations in the superquadratic case Li, Dingding Zhang, Chao Analysis of PDEs We investigate the interior Sobolev regularity of weak solutions to the nonlocal $(1, p)$-Laplace equations in the superquadratic case $p\ge 2$. As a product, the explicit Hölder continuity estimates of weak solutions are derived. The proof relies on a detailed analysis of the structural characteristics of $(1, p)$-growth in the nonlocal setting, combined with the finite difference quotient method, tail estimates, refined energy estimates, and a Moser-type iteration scheme. |
| title | Sobolev regularity for the nonlocal $(1, p)$-Laplace equations in the superquadratic case |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.23288 |