{"paper":{"title":"A critical Hardy-Rellich inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Hern\\'an Castro","submitted_at":"2025-11-20T16:52:15Z","abstract_excerpt":"In this work, we prove a critical version of a Hardy-Rellich type inequality. We show that for $N\\geq 1$ there exists a constant $C_N>0$ such that \\[ \\int_{\\mathbb R^N}\\left|\\nabla\\left(\\frac{u(x)}{|x|}\\right)\\right|^N\\,\\mathrm{d}x\\leq C_N\\int_{\\mathbb R^N}\\left|\\Delta u(x)\\right|^N\\,\\mathrm{d}x, \\] for any $u\\in C^\\infty_c(\\mathbb R^N\\setminus\\left\\{0\\right\\})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.16537","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/2511.16537/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"}