{"paper":{"title":"Gradient stability of Caffarelli-Kohn-Nirenberg inequality involving weighted p-Laplace","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":"2024-01-05T14:52:22Z","abstract_excerpt":"The best constant and extremal functions are well known of the following Caffarelli-Kohn-Nirenberg inequality \\[ \\int_{\\mathbb{R}^N}|\\nabla u|^p\\frac{\\mathrm{d}x}{|x|^{\\mu}}\\geq \\mathcal{S} \\left(\\int_{\\mathbb{R}^N}|u|^r\\frac{\\mathrm{d}x}{|x|^s} \\right)^{\\frac{p}{r}}, \\quad \\mbox{for all}\\quad u\\in C^\\infty_c(\\mathbb{R}^N), \\] where $1<p<p+\\mu<N$, $\\frac{\\mu}{p}\\leq \\frac{s}{r}<\\frac{\\mu}{p}+1$, $r=\\frac{p(N-s)}{N-p-\\mu}$. An important task is investigating the stability of extremals for this inequality. Firstly, we give the classification to the linearized problem related to the extremals whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.04129","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/2401.04129/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"}