{"paper":{"title":"On the stability of critical points of the Hardy-Littlewood-Sobolev inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kuan Liu, Qian Zhang, Wenming Zou","submitted_at":"2023-06-28T01:31:15Z","abstract_excerpt":"This paper is concerned with the quantitative stability of critical points of the Hardy-Littlewood-Sobolev inequality. Namely, we give quantitative estimates for the Choquard equation: $$-\\Delta u=(I_{\\mu}\\ast|u|^{2_\\mu^*}) u^{2_\\mu^*-1}\\ \\ \\text{in}\\ \\ \\R^N,$$ where $u>0,\\ N\\geq 3,\\ \\mu\\in(0,N)$, $I_{\\mu}$ is the Riesz potential and $2_\\mu^* \\coloneqq \\frac{2N-\\mu}{N-2}$ is the upper Hardy-Littlewood-Sobolev critical exponent. The Struwe's decomposition (see M. Struwe: Math Z.,1984) showed that the equation $\\Delta u + u^{\\frac{N+2}{N-2 }}=0$ has phenomenon of ``stable up to bubbling'', that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.15862","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/2306.15862/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"}