{"paper":{"title":"Uniform Boundary Estimates in Homogenization of Higher Order Elliptic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Weisheng Niu, Yao Xu","submitted_at":"2017-09-13T01:09:48Z","abstract_excerpt":"This paper focuses on the uniform boundary estimates in homogenization of a family of higher order elliptic operators $\\mathcal{L}_\\epsilon$, with rapidly oscillating periodic coefficients. We derive uniform boundary $C^{m-1,\\lambda} (0\\!<\\!\\lambda\\!<\\!1)$, $ W^{m,p}$ estimates in $C^1$ domains, as well as uniform boundary $C^{m-1,1}$ estimate in $C^{1,\\theta} (0\\!<\\!\\theta\\!<\\!1)$ domains without the symmetry assumption on the operator. The proof, motivated by the profound work \"S.N. Armstrong and C.~K. Smart, Ann. Sci. \\'Ec. Norm. Sup\\'er. (2016), Z. Shen, Anal. PDE (2017)\", is based on a su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04097","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"}