{"paper":{"title":"Optimal convergence rates in multiscale elliptic homogenization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jinping Zhuge, Weisheng Niu, Yao Xu","submitted_at":"2025-09-11T12:44:40Z","abstract_excerpt":"This paper is devoted to the quantitative homogenization of multiscale elliptic operator $-\\nabla\\cdot A_\\varepsilon \\nabla$, where $A_\\varepsilon(x) = A(x/\\varepsilon_1, x/\\varepsilon_2,\\cdots, x/\\varepsilon_n)$, $\\varepsilon = (\\varepsilon_1, \\varepsilon_2,\\cdots, \\varepsilon_n) \\in (0,1]^n$ and $\\varepsilon_i > \\varepsilon_{i+1}$. We assume that $A(y_1,y_2,\\cdots, y_n)$ is 1-periodic in each $y_i \\in \\mathbb{R}^d$ and real analytic. Classically, the method of reiterated homogenization has been applied to study this multiscale elliptic operator, which leads to a convergence rate limited by t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.09410","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.09410/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}