{"paper":{"title":"The isoperimetric problem for a class of non-radial weights and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angelo Alvino, Anna Mercaldo, Francesco Chiacchio, Friedemann Brock, Maria Rosaria Posteraro","submitted_at":"2018-05-04T15:49:36Z","abstract_excerpt":"We study a class of isoperimetric problems on $\\mathbb{R}^{N}_{+} $ where the densities of the weighted volume and weighted perimeter are given by two different non-radial functions of the type $|x|^k x_N^\\alpha$. Our results imply some sharp functional inequalities, like for instance, Caffarelli-Kohn-Nirenberg type inequalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02518","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":""},"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"}