{"paper":{"title":"On vanishing and localizing of transmission eigenfunctions near singular points: a numerical study","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP","math.SP"],"primary_cat":"math.NA","authors_text":"Eemeli Bl{\\aa}sten, Hongyu Liu, Xiaofei Li, Yuliang Wang","submitted_at":"2017-04-06T15:15:35Z","abstract_excerpt":"This paper is concerned with the intrinsic geometric structure of interior transmission eigenfunctions arising in wave scattering theory. We numerically show that the aforementioned geometric structure can be much delicate and intriguing. The major findings can be roughly summarized as follows. If there is a cusp on the support of the underlying potential function, then the interior transmission eigenfunction vanishes near the cusp if its interior angle is less than $\\pi$, whereas the interior transmission eigenfunction localizes near the cusp if its interior angle is bigger than $\\pi$. Furthe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01885","kind":"arxiv","version":3},"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"}