{"paper":{"title":"An effective Hamiltonian for the eigenvalue asymptotics of a Robin Laplacian with a large parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Konstantin Pankrashkin, Nicolas Popoff","submitted_at":"2015-02-03T14:44:19Z","abstract_excerpt":"We consider the Laplacian on a class of smooth domains $\\Omega\\subset \\mathbb{R}^{\\nu}$, $\\nu\\ge 2$, with attractive Robin boundary conditions: \\[ Q^\\Omega_\\alpha u=-\\Delta u, \\quad \\dfrac{\\partial u}{\\partial n}=\\alpha u \\text{ on } \\partial\\Omega, \\ \\alpha>0, \\] where $n$ is the outer unit normal, and study the asymptotics of its eigenvalues $E_{j}(Q^\\Omega_\\alpha)$ as well as some other spectral properties for $\\alpha\\to+\\infty$ We work with both compact domains and non-compact ones with a suitable behavior at infinity. For domains with compact $C^2$ boundaries and fixed $j$, we show that \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00877","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"}