{"paper":{"title":"On vanishing near corners of transmission eigenfunctions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Eemeli Bl{\\aa}sten, Hongyu Liu","submitted_at":"2017-01-27T06:53:51Z","abstract_excerpt":"Let $\\Omega$ be a bounded domain in $\\mathbb{R}^n$, $n\\geq 2$, and $V\\in L^\\infty(\\Omega)$ be a potential function. Consider the following transmission eigenvalue problem for nontrivial $v, w\\in L^2(\\Omega)$ and $k\\in\\mathbb{R}_+$, \\[(\\Delta+k^2)v= 0 \\quad \\text{in } \\Omega,\\] \\[(\\Delta+k^2(1+V))w= 0 \\quad \\text{in } \\Omega,\\] \\[w-v \\in H^2_0(\\Omega), \\quad \\lVert v \\rVert_{L^2(\\Omega)}=1. \\] We show that the transmission eigenfunctions $v$ and $w$ carry the geometric information of $\\mathrm{supp}(V)$. Indeed, it is proved that $v$ and $w$ vanish near a corner point on $\\partial \\Omega$ in a g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07957","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"}