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Based upon the convergence rates, an interior Lipschitz estimate, as well as a boundary H\\\"older estimate can be developed at large scales without any smoothness assumption, and these will implies reverse H\\\"older estimates established for a $C^1$ domain. By a real method developed by Z.Shen \\cite{S3}, we consequently derive a g"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1807.10865","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-28T01:21:10Z","cross_cats_sorted":[],"title_canon_sha256":"74c27d9027a6a1088400133de0c97a8800a778931295e5c22348255930d3bf3c","abstract_canon_sha256":"ef9b795fce08ebb4e9963aa332fddaa4869fb6fee24d70cad34fda7ff4e9f3f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:37.199683Z","signature_b64":"WsNIpiSlwqBt0JNOM83JH0NmlQ8MFq+b/fWEI5LWfMPimNtmNvwBHg837o0W3Xb6rNRrMAuN9WndkTBjxcafDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1b242fd49cb5a04eacaa543f573dd669346cb5331e057ae9b5765549cf224f9","last_reissued_at":"2026-05-18T00:09:37.199224Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:37.199224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantitative Estimates on Periodic Homogenization of Nonlinear Elliptic Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Li Wang, Peihao Zhao, Qiang Xu","submitted_at":"2018-07-28T01:21:10Z","abstract_excerpt":"In this paper, we are interested in the periodic homogenization of quasilinear elliptic equations. We obtain error estimates $O(\\varepsilon^{1/2})$ for a $C^{1,1}$ domain, and $O(\\varepsilon^\\sigma)$ for a Lipschitz domain, in which $\\sigma\\in(0,1/2)$ is close to zero. Based upon the convergence rates, an interior Lipschitz estimate, as well as a boundary H\\\"older estimate can be developed at large scales without any smoothness assumption, and these will implies reverse H\\\"older estimates established for a $C^1$ domain. 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