{"paper":{"title":"Oscillating behaviour of the spectrum for a plasmonic problem in a domain with a rounded corner","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lucas Chesnel, Sergei A. Nazarov, Xavier Claeys","submitted_at":"2015-12-09T16:11:25Z","abstract_excerpt":"We investigate the eigenvalue problem $-\\text{div}(\\sigma \\nabla u) = \\lambda u\\ (\\mathscr{P})$ in a 2D domain $\\Omega$ divided into two regions $\\Omega_{\\pm}$. We are interested in situations where $\\sigma$ takes positive values on $\\Omega_{+}$ and negative ones on $\\Omega_{-}$. Such problems appear in time harmonic electromagnetics in the modeling of plasmonic technologies. In a recent work [15], we highlighted an unusual instability phenomenon for the source term problem associated with $(\\mathscr{P})$: for certain configurations, when the interface between the subdomains $\\Omega_{\\pm}$ pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02920","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"}