{"paper":{"title":"On existence of minimizers for weighted $L^p$-Hardy inequalities on $C^{1,\\gamma}$-domains with compact boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.SP"],"primary_cat":"math.AP","authors_text":"Baptiste Devyver, Ujjal Das, Yehuda Pinchover","submitted_at":"2023-03-06T22:28:07Z","abstract_excerpt":"Let $p \\in (1,\\infty)$, $\\alpha\\in \\mathbb{R}$, and $\\Omega\\subsetneq \\mathbb{R}^N$ be a $C^{1,\\gamma}$-domain with a compact boundary $\\partial \\Omega$, where $\\gamma\\in (0,1]$. Denote by $\\delta_{\\Omega}(x)$ the distance of a point $x\\in \\Omega$ to $\\partial \\Omega$. Let $\\widetilde{W}^{1,p;\\alpha}_0(\\Omega)$ be the closure of $C_c^{\\infty}(\\Omega)$ in $\\widetilde{W}^{1,p;\\alpha}(\\Omega)$, where\n  $$\\widetilde{W}^{1,p;\\alpha}(\\Omega):= \\left\\{\\varphi \\in {W}^{1,p}_{\\mathrm{loc}} (\\Omega) \\mid \\left( \\| \\, |\\nabla \\varphi \\, |\\|_{L^p(\\Omega;\\delta_{\\Omega}^{-\\alpha})}^p + \\|\\varphi\\|_{L^p(\\Om"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.03527","kind":"arxiv","version":3},"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/2303.03527/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"}