{"paper":{"title":"Plummeting and blinking eigenvalues of the Robin Laplacian in a cuspidal domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Jari Taskinen, Nicolas Popoff, Sergei A. Nazarov","submitted_at":"2018-09-28T11:14:48Z","abstract_excerpt":"We consider the Robin Laplacian in the domains $\\Omega$ and $\\Omega^\\varepsilon$, $\\varepsilon >0$, with sharp and blunted cusps, respectively. Assuming that the Robin coefficient $a$ is large enough, the spectrum of the problem in $\\Omega$ is known to be residual and to cover the whole complex plane, but on the contrary, the spectrum in the Lipschitz domain $\\Omega^\\varepsilon$ is discrete. However, our results reveal the strange behavior of the discrete spectrum as the blunting parameter $\\varepsilon$ tends to 0: we construct asymptotic forms of the eigenvalues and detect families of \"hardly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10963","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"}