{"paper":{"title":"Eigenvalue counting function for Robin Laplacians on conical domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Konstantin Pankrashkin, Nicolas Popoff, Vincent Bruneau","submitted_at":"2016-02-24T09:47:46Z","abstract_excerpt":"We study the discrete spectrum of the Robin Laplacian $Q^{\\Omega}_\\alpha$ in $L^2(\\Omega)$, \\[ u\\mapsto -\\Delta u, \\quad \\dfrac{\\partial u}{\\partial n}=\\alpha u \\text{ on }\\partial\\Omega, \\] where $\\Omega\\subset \\mathbb{R}^{3}$ is a conical domain with a regular cross-section $\\Theta\\subset \\mathbb{S}^2$, $n$ is the outer unit normal, and $\\alpha>0$ is a fixed constant. It is known from previous papers that the bottom of the essential spectrum of $Q^{\\Omega}_\\alpha$ is $-\\alpha^2$ and that the finiteness of the discrete spectrum depends on the geometry of the cross-section. We show that the ac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07448","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":""},"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"}