Sharp gradient integrability for $(s,p)$-Poisson type equations
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866912891394850816 |
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| author | Bögelein, Verena Duzaar, Frank Liao, Naian Moring, Kristian |
| author_facet | Bögelein, Verena Duzaar, Frank Liao, Naian Moring, Kristian |
| contents | We prove local $W^{1,q}$-regularity for weak solutions to fractional $p$-Laplacian type equations with right-hand side $f\in L^r_{\mathrm{loc}}(Ω)$. Assuming $p>1$, $s\in(0,1)$, and $sp'>1$, solutions belong to $W^{1,q}_{\mathrm{loc}}(Ω)$ for the optimal exponent $q=q(n,p,s,r)$. We obtain quantitative local gradient estimates involving nonlocal tail terms. The optimality of $q$ is confirmed by a counterexample. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08944 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp gradient integrability for $(s,p)$-Poisson type equations Bögelein, Verena Duzaar, Frank Liao, Naian Moring, Kristian Analysis of PDEs We prove local $W^{1,q}$-regularity for weak solutions to fractional $p$-Laplacian type equations with right-hand side $f\in L^r_{\mathrm{loc}}(Ω)$. Assuming $p>1$, $s\in(0,1)$, and $sp'>1$, solutions belong to $W^{1,q}_{\mathrm{loc}}(Ω)$ for the optimal exponent $q=q(n,p,s,r)$. We obtain quantitative local gradient estimates involving nonlocal tail terms. The optimality of $q$ is confirmed by a counterexample. |
| title | Sharp gradient integrability for $(s,p)$-Poisson type equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.08944 |