{"paper":{"title":"On the stability constant of Caffarelli-Kohn-Nirenberg inequality","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shengbing Deng, Xingliang Tian","submitted_at":"2023-08-08T07:53:21Z","abstract_excerpt":"By using a spectral analysis, we first show that the Caffarelli--Kohn--Nirenberg inequality with gradient remainder term of any order less than $4$ does not hold on the {\\em Felli-Schneider} curve $b_{\\mathrm{FS}}(a)$. Furthermore, we prove the existence of minimizers of sharp stability constant of Caffarelli--Kohn--Nirenberg inequality near the new curve $b^*_{\\mathrm{FS}}(a)(>b_{\\mathrm{FS}}(a))$, which extends the work of Wei and Wu [Math. Z., 2024] to a sightly larger region."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.04111","kind":"arxiv","version":4},"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/2308.04111/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"}