{"paper":{"title":"Sharp anisotropic $L^2$-Caffarelli-Kohn-Nirenberg inequalities associated with the Minkowski functional","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Zhenzhen Wei","submitted_at":"2026-07-28T15:39:21Z","abstract_excerpt":"Let $K\\subset \\RN$ be a convex body containing the origin in its interior, and let $\\hK{\\cdot}$ be its Minkowski functional. In this paper, we develop an identity-based framework for sharp anisotropic $L^2$-Caffarelli-Kohn-Nirenberg inequalities associated with the anisotropic radial derivative $$ \\mathcal R_K(u)(x)=\\frac{x\\cdot\\nabla u(x)}{\\hK{x}}, \\quad x\\in\\RN\\setminus\\{o\\}. $$ A key point of the present work is that $K$ is not assumed to be origin-symmetric. Consequently, the Minkowski functional $\\hK{\\cdot}$ need not be even, and the usual norm-based anisotropic arguments do not apply dir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25876","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/2607.25876/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"}