{"paper":{"title":"Non-degeneracy, stability and symmetry for the fractional Caffarelli-Kohn-Nirenberg inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Federico Glaudo, Nicola De Nitti, Tobias K\\\"onig","submitted_at":"2024-03-04T18:33:39Z","abstract_excerpt":"The fractional Caffarelli-Kohn-Nirenberg inequality states that $$ \\int_{\\mathbb{R}^n}\\int_{\\mathbb{R}^n} \\frac{(u(x)-u(y))^2}{|x|^\\alpha |x-y|^{n+2s} |y|^\\alpha} \\mathrm{d} x \\, \\mathrm{d} y\n  \\geq \\Lambda_{n, s, p, \\alpha,\\beta}\n  \\|u |x|^{-\\beta}\\|_{L^p}^2, $$ for $0<s<\\min\\{1, n/2\\}$, $2<p<2^*_s$, and $\\alpha,\\beta\\in\\mathbb R$ so that $\\beta-\\alpha = s - n\\big(\\frac12 - \\frac1p\\big)$ and $-2s < \\alpha < \\frac{n-2s}{2}$.\n  Continuing the program started in Ao et al. (2022), we establish the non-degeneracy and sharp quantitative stability of minimizers for $\\alpha\\ge 0$. Furthermore, we sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.02303","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/2403.02303/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"}