{"paper":{"title":"Modica type estimates and curvature results for overdetermined $p$-Laplace problems","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jing Wu, Yuanyuan Lian","submitted_at":"2025-06-17T14:37:00Z","abstract_excerpt":"In this paper we prove Modica type estimates for the following overdetermined $p$-Laplace problem \\begin{equation*}\n  \\begin{cases}\n  \\mathrm{div} \\left(|\\nabla u|^{p-2}\\nabla u\\right)+f(u) =0& \\mbox{in $\\Omega$, }\n  u>0 &\\mbox{in $\\Omega$, }\n  u=0 &\\mbox{on $\\partial\\Omega$, }\n  \\partial_{\\nu} u=-\\kappa &\\mbox{on $\\partial\\Omega$, }\n  \\end{cases} \\end{equation*} where $1<p<+\\infty$, $f\\in C^1(\\mathbb{R})$, $\\Omega \\subset \\mathbb{R}^n$ ($n\\geq 2$) is a $C^1$ domain (bounded or unbounded), $\\nu$ is the exterior unit normal of $\\partial \\Omega$ and $\\kappa\\geq 0$ is a constant. Based on Modica "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.14579","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/2506.14579/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"}