{"paper":{"title":"Stability of the Caffarelli-Kohn-Nirenberg inequality along Felli-Schneider curve: critical points at infinity","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Yunze Wu","submitted_at":"2024-07-28T02:24:44Z","abstract_excerpt":"In this paper, we consider the following Caffarelli-Kohn-Nirenberg (CKN for short) inequality \\begin{eqnarray*} \\bigg(\\int_{{\\mathbb R}^d}|x|^{-b(p+1)}|u|^{p+1}dx\\bigg)^{\\frac{2}{p+1}}\\leq S_{a,b}\\int_{{\\mathbb R}^d}|x|^{-2a}|\\nabla u|^2dx, \\end{eqnarray*} where $u\\in D^{1,2}_{a}({\\mathbb R}^d)$, $d\\geq2$, $p=\\frac{d+2(1+a-b)}{d-2(1+a-b)}$ and \\begin{eqnarray}\\label{eq0003} \\left\\{\\aligned &a<b<a+1,\\quad d=2,\\\\ &a\\leq b<a+1,\\quad d\\geq3. \\endaligned \\right. \\end{eqnarray} Based on the ideas of \\cite{DSW2024,FP2024}, we develop a suitable strategy to derive the following sharp stability of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.19366","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.19366/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"}