{"paper":{"title":"Gradient estimates for the fractional $p$-Poisson equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Frank Duzaar, Kristian Moring, Naian Liao, Verena B\\\"ogelein","submitted_at":"2025-03-07T19:53:26Z","abstract_excerpt":"We consider local weak solutions to the fractional $p$-Poisson equation of order $s$, i.e. $\\left( - \\Delta_p\\right)^s u = f$. In the range $p>1$ and $s\\in \\big(\\frac{p-1}{p},1\\big)$ we prove Calder\\'on & Zygmund type estimates at the gradient level. More precisely, we show for any $q>1$ that \\begin{equation*}\n  f\\in L^{\\frac{qp}{p-1}}_{\\rm loc}\n  \\quad\\Longrightarrow\\quad\n  \\nabla u\\in L^{qp}_{\\rm loc}. \\end{equation*} The qualitative result is accompanied by a local quantitative estimate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.05903","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.05903/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}