{"paper":{"title":"Spectral properties of elliptic operator with double-contrast coefficients near a hyperplane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Andrii Khrabustovskyi, Michael Plum","submitted_at":"2014-04-09T17:22:34Z","abstract_excerpt":"In this paper we study the asymptotic behaviour as $\\varepsilon\\to 0$ of the spectrum of the elliptic operator $\\mathcal{A}^\\varepsilon=-{1\\over b^\\varepsilon}\\mathrm{div}(a^\\varepsilon\\nabla)$ posed in a bounded domain $\\Omega\\subset\\mathbb{R}^n$ $(n \\geq 2)$ subject to Dirichlet boundary conditions on $\\partial\\Omega$. When $\\varepsilon\\to 0$ both coefficients $a^\\varepsilon$ and $b^\\varepsilon$ become high contrast in a small neighborhood of a hyperplane $\\Gamma$ intersecting $\\Omega$. We prove that the spectrum of $\\mathcal{A}^\\varepsilon$ converges to the spectrum of an operator acting in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2555","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"}