{"paper":{"title":"Homogenization of the Dirichlet problem for elliptic systems: Two-parametric error estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tatiana Suslina, Yulia Meshkova","submitted_at":"2017-02-02T06:27:54Z","abstract_excerpt":"Let $\\mathcal{O}\\subset\\mathbb{R}^d$ be a bounded domain of class $C^{1,1}$. In $L_2(\\mathcal{O};\\mathbb{C}^n)$, we study a selfadjoint matrix elliptic second order differential operator $B_{D,\\varepsilon}$, $0<\\varepsilon\\leqslant 1$, with the Dirichlet boundary condition. The principal part of the operator is given in a factorized form. The operator involves lower order terms with unbounded coefficients. The coefficients of $B_{D,\\varepsilon}$ are periodic and depend on $\\mathbf{x}/\\varepsilon$. We study the generalized resolvent $\\left(B_{D,\\varepsilon}-\\zeta Q_0(\\cdot/\\varepsilon)\\right)^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00550","kind":"arxiv","version":4},"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"}