{"paper":{"title":"Uniform stability of the Dirichlet spectrum for rough outer perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Alexandre Girouard, Bruno Colbois, Mette Iversen","submitted_at":"2012-06-12T18:44:58Z","abstract_excerpt":"The goal of this paper is to study the Dirichlet eigenvalues of bounded domains $\\Omega\\subset \\Omega'$. With a local spectral stability requirement on $\\Omega$, we show that the difference of the Dirichlet eigenvalues of $\\Omega'$ and $\\Omega$ is explicitly controlled from above in terms of the first eigenvalue of $\\Omega'\\setminus\\bar{\\Omega}$ and of geometric constants depending on the inner domain $\\Omega$. In particular, $\\Omega'$ can be an arbitrary bounded domain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2616","kind":"arxiv","version":1},"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"}