{"paper":{"title":"Non-radial minimizers for Hardy--Sobolev inequalities in non-convex cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. I. Nazarov, N. V. Rastegaev","submitted_at":"2025-07-06T17:18:14Z","abstract_excerpt":"The symmetry breaking is obtained for Neumann problems driven by $p$-Laplacian in certain non-convex cones. These problems are generated by the Hardy--Sobolev inequalities. In the case of the Sobolev inequality for the ordinary Laplacian this problem was investigated in (Ciraolo, Pacella, Polvara, 2024).\n  Such problems have obvious radial solutions -- Talenti--Bliss type functions of $|x|$. However, under a certain restriction on the first Neumann eigenvalue $\\lambda_1(D)$ of the Beltrami--Laplace operator on the spherical cross-section $D$ of the cone we prove this radial solution cannot be "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04470","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/2507.04470/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"}