{"paper":{"title":"First-order expansion for the Dirichlet eigenvalues of an elliptic system with oscillating coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christophe Prange","submitted_at":"2011-11-10T17:03:18Z","abstract_excerpt":"This paper is concerned with the homogenization of the Dirichlet eigenvalue problem, posed in a bounded domain $\\Omega\\subset\\mathbb R^2$, for a vectorial elliptic operator $-\\nabla\\cdot A^\\epsilon(\\cdot)\\nabla$ with $\\epsilon$-periodic coefficients. We analyse the asymptotics of the eigenvalues $\\lambda^{\\epsilon,k}$ when $\\epsilon\\rightarrow 0$, the mode $k$ being fixed. A first-order asymptotic expansion is proved for $\\lambda^{\\epsilon,k}$ in the case when $\\Omega$ is either a smooth uniformly convex domain, or a convex polygonal domain with sides of slopes satisfying a small divisors assu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2517","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"}