{"paper":{"title":"Homogenization of high order elliptic operators with periodic coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrey Kukushkin, Tatiana Suslina","submitted_at":"2015-11-13T12:31:51Z","abstract_excerpt":"In $L_2({\\mathbb R}^d;{\\mathbb C}^n)$, we study a selfadjoint strongly elliptic operator $A_\\varepsilon$ of order $2p$ given by the expression $b({\\mathbf D})^* g({\\mathbf x}/\\varepsilon) b({\\mathbf D})$, $\\varepsilon >0$. Here $g({\\mathbf x})$ is a bounded and positive definite $(m\\times m)$-matrix-valued function in ${\\mathbb R}^d$; it is assumed that $g({\\mathbf x})$ is periodic with respect to some lattice. Next, $b({\\mathbf D})=\\sum_{|\\alpha|=p}^d b_\\alpha {\\mathbf D}^\\alpha$ is a differential operator of order $p$ with constant coefficients; $b_\\alpha$ are constant $(m\\times n)$-matrices"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04260","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"}