{"paper":{"title":"Homogenization of the Neumann problem for elliptic systems with periodic coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tatiana Suslina","submitted_at":"2012-12-05T20:23:23Z","abstract_excerpt":"Let ${\\mathcal O} \\subset {\\mathbb R}^d$ be a bounded domain with the boundary of class $C^{1,1}$. In $L_2({\\mathcal O};{\\mathbb C}^n)$, a matrix elliptic second order differential operator ${\\mathcal A}_{N,\\varepsilon}$ with the Neumann boundary condition is considered. Here $\\varepsilon>0$ is a small parameter, the coefficients of ${\\mathcal A}_{N,\\varepsilon}$ are periodic and depend on ${\\mathbf x} /\\varepsilon$. There are no regularity assumptions on the coefficients. It is shown that the resolvent $({\\mathcal A}_{N,\\varepsilon}+\\lambda I)^{-1}$ converges in the $L_2({\\mathcal O};{\\mathbb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1148","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"}