{"paper":{"title":"Spectrum of a diffusion operator with coefficient changing sign over a small inclusion","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":"2014-01-09T20:36:35Z","abstract_excerpt":"We study a spectral problem $(\\mathscr{P}^{\\delta})$ for a diffusion like equation in a 3D domain $\\Omega$. The main originality lies in the presence of a parameter $\\sigma^{\\delta}$, whose sign changes on $\\Omega$, in the principal part of the operator we consider. More precisely, $\\sigma^{\\delta}$ is positive on $\\Omega$ except in a small inclusion of size $\\delta>0$. Because of the sign-change of $\\sigma^{\\delta}$, for all $\\delta>0$ the spectrum of $(\\mathscr{P}^{\\delta})$ consists of two sequences converging to $\\pm\\infty$. However, at the limit $\\delta=0$, the small inclusion vanishes so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2146","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"}