{"paper":{"title":"Sharp Hardy and Hardy--Sobolev inequalities with point singularities on the boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Achilles Tertikas, Gerassimos Barbatis, Stathis Filippas","submitted_at":"2017-01-23T11:27:02Z","abstract_excerpt":"We study the Hardy inequality when the singularity is placed on the boundary of a bounded domain in $\\mathbb{R}^n$ that satisfies both an interior and exterior ball condition at the singularity. We obtain the sharp Hardy constant $n^2/4$ in case the exterior ball is large enough and show the necessity of the large exterior ball condition. We improve Hardy inequality with the best constant by adding a sharp Sobolev term. We next produce criteria that lead to characterizing maximal potentials that improve Hardy inequality. Breaking the criteria one produces successive improvements with sharp con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06336","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"}