{"paper":{"title":"Weighted Hardy inequality with higher dimensional singularity on the boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fethi Mahmoudi, Mouhamed Moustapha Fall","submitted_at":"2012-01-31T21:27:38Z","abstract_excerpt":"Let $\\Omega$ be a smooth bounded domain in $\\mahbb R^N$ with $N\\ge 3$ and let $\\Sigma_k$ be a closed smooth submanifold of $\\delta \\Omega$ of dimension $1\\le k\\le N-2$. In this paper we study the weighted Hardy inequality with weight function singular on $\\Sigma_k$. In particular we provide sufficient and necessary conditions for existence of minimizers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0033","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":""},"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"}