{"paper":{"title":"Rellich inequalities with weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Paolo Caldiroli, Roberta Musina","submitted_at":"2011-03-31T13:57:21Z","abstract_excerpt":"Let $\\Omega$ be a cone in $\\mathbb{R}^{n}$ with $n\\ge 2$. For every fixed $\\alpha\\in\\mathbb{R}$ we find the best constant in the Rellich inequality $\\int_{\\Omega}|x|^{\\alpha}|\\Delta u|^{2}dx\\ge C\\int_{\\Omega}|x|^{\\alpha-4}|u|^{2}dx$ for $u\\in C^{2}_{c}(\\bar\\Omega\\setminus\\{0\\})$. We also estimate the best constant for the same inequality on $C^{2}_{c}(\\Omega)$. Moreover we show improved Rellich inequalities with remainder terms involving logarithmic weights on cone-like domains."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.6184","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":""},"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"}