{"paper":{"title":"Resolvent estimates for high-contrast elliptic problems with periodic coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kirill Cherednichenko, Shane Cooper","submitted_at":"2014-04-21T22:07:13Z","abstract_excerpt":"We study the asymptotic behaviour of the resolvents $({\\mathcal A}^\\varepsilon+I)^{-1}$ of elliptic second-order differential operators ${\\mathcal A}^\\varepsilon$ in ${\\mathbb R}^d$ with periodic rapidly oscillating coefficients, as the period $\\varepsilon$ goes to zero. The class of operators covered by our analysis includes both the \"classical\" case of uniformly elliptic families (where the ellipticity constant does not depend on $\\varepsilon$) and the \"double-porosity\" case of coefficients that take contrasting values of order one and of order $\\varepsilon^2$ in different parts of the perio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5342","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"}