{"paper":{"title":"Existence of Bianchi-Egnell stability extremizer for the Hardy-Sobolev inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Debabrata Karmakar, Monideep Ghosh, Souptik Chakraborty","submitted_at":"2025-05-11T16:21:29Z","abstract_excerpt":"In this article, we prove the best Bianchi-Egnell constant for the Hardy-Sobolev (HS) inequality \\begin{align*} C_{\\tiny\\mbox{{BE}}}(\\gamma) := \\inf_{{u \\ \\small \\mbox{not an optimizer}}} \\frac{\\int_{\\mathbb{R}^n} \\left(|\\nabla u|^2 - \\frac{\\gamma}{|x|^2}u^2\\right) \\ {\\rm d}x - S_{\\gamma}\\|u\\|_{L^{2^{\\star}}}^2}{\\mbox{dist} (u, \\ \\mbox{set of optimizers})^2}, \\end{align*} is attained, extending the result of K\\\"onig [arXiv:2211.14185] for the classical Sobolev inequality (that corresponds to $\\gamma = 0$). One of the main difficulties is that the third eigenspace of the linearized operator may"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.07039","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.07039/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"}