{"paper":{"title":"Lipschitz regularity of fractional $p$-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anup Biswas, Erwin Topp","submitted_at":"2025-04-13T06:52:52Z","abstract_excerpt":"In this article, we investigate the H\\\"{o}lder regularity of the fractional $p$-Laplace equation of the form $(-\\Delta_p)^s u=f$ where $p>1, s\\in (0, 1)$ and $f\\in L^\\infty_{\\rm loc}(\\Omega)$. Specifically, we prove that $u\\in C^{0, \\gamma_\\circ}_{\\rm loc}(\\Omega)$ for $\\gamma_\\circ=\\min\\{1, \\frac{sp}{p-1}\\}$, provided that $\\frac{sp}{p-1}\\neq 1$. In particular, it shows that $u$ is locally Lipschitz for $\\frac{sp}{p-1}>1$. Moreover, we show that for $\\frac{sp}{p-1}=1$, the solution is locally Lipschitz, provided that $f$ is locally H\\\"{o}lder continuous. Additionally, we discuss further regul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.09457","kind":"arxiv","version":2},"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/2504.09457/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"}