{"paper":{"title":"Embedded eigenvalues of the Neumann problem in a strip with a box-shaped perturbation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"G. Cardone, S.A. Nazarov, T. Durante","submitted_at":"2015-12-21T22:15:05Z","abstract_excerpt":"We consider the spectral Neumann problem for the Laplace operator in an acoustic waveguide $\\Pi_{l}^{\\varepsilon}$ obtained from a straight unit strip by a low box-shaped perturbation of size $2l\\times\\varepsilon,$ where $\\varepsilon>0$ is a small parameter. We prove the existence of the length parameter $l_{k}^{\\varepsilon}=\\pi k+O\\left( \\varepsilon\\right) $ with any $k=1,2,3,...$ such that the waveguide $\\Pi_{l_{k}^{\\varepsilon}}^{\\varepsilon }$ supports a trapped mode with an eigenvalue $\\lambda_{k}^{\\varepsilon}% =\\pi^{2}-4\\pi^{4}l^{2}\\varepsilon^{2}+O\\left( \\varepsilon^{3}\\right) $ embedd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06891","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"}