{"paper":{"title":"Homogenization of elliptic problems: error estimates in dependence of the spectral parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tatiana Suslina","submitted_at":"2014-06-29T17:35:45Z","abstract_excerpt":"We consider a strongly elliptic differential expression of the form $b(D)^* g(x/\\varepsilon) b(D)$, $\\varepsilon >0$, where $g(x)$ is a matrix-valued function in ${\\mathbb R}^d$ assumed to be bounded, positive definite and periodic with respect to some lattice; $b(D)=\\sum_{l=1}^d b_l D_l$ is the first order differential operator with constant coefficients. The symbol $b(\\xi)$ is subject to some condition ensuring strong ellipticity. The operator given by $b(D)^* g(x/\\varepsilon) b(D)$ in $L_2({\\mathbb R}^d;{\\mathbb C}^n)$ is denoted by $A_\\varepsilon$. Let ${\\mathcal O} \\subset {\\mathbb R}^d$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7530","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"}