{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:DXA2ME5CFS5ORUX6BKX3J4OC3U","short_pith_number":"pith:DXA2ME5C","schema_version":"1.0","canonical_sha256":"1dc1a613a22cbae8d2fe0aafb4f1c2dd37e31ee9ef3f7d7ebad7021e4dd876aa","source":{"kind":"arxiv","id":"1707.03160","version":1},"attestation_state":"computed","paper":{"title":"Regularity of Homogenized Boundary Data in Periodic Homogenization of Elliptic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jinping Zhuge, Zhongwei Shen","submitted_at":"2017-07-11T08:04:44Z","abstract_excerpt":"This paper is concerned with periodic homogenization of second-order elliptic systems in divergence form with oscillating Dirichlet data or Neumann data of first order. We prove that the homogenized boundary data belong to $W^{1, p}$ for any $1<p<\\infty$. In particular, this implies that the boundary layer tails are H\\\"older continuous of order $\\alpha$ for any $\\alpha \\in (0,1)$."},"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":"1707.03160","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-11T08:04:44Z","cross_cats_sorted":[],"title_canon_sha256":"f046deedd7e45402d283b5e4c11cf8df543bad7cfab7c2177bba58b5b2c83c5a","abstract_canon_sha256":"8a6d47ca98c81a7a37d650d0dbfc448916e220981e993a40fe3235928bc773b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:29.742423Z","signature_b64":"iJ5fmTH9QCJhHQ5V9fXXZY+4br+whVMGWx4ljoi21OGCUitc7/3fSUkiM9SEJstO0Uzswn2cWkjzl2tAiIc7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dc1a613a22cbae8d2fe0aafb4f1c2dd37e31ee9ef3f7d7ebad7021e4dd876aa","last_reissued_at":"2026-05-18T00:40:29.741882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:29.741882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularity of Homogenized Boundary Data in Periodic Homogenization of Elliptic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jinping Zhuge, Zhongwei Shen","submitted_at":"2017-07-11T08:04:44Z","abstract_excerpt":"This paper is concerned with periodic homogenization of second-order elliptic systems in divergence form with oscillating Dirichlet data or Neumann data of first order. We prove that the homogenized boundary data belong to $W^{1, p}$ for any $1<p<\\infty$. In particular, this implies that the boundary layer tails are H\\\"older continuous of order $\\alpha$ for any $\\alpha \\in (0,1)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03160","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.03160","created_at":"2026-05-18T00:40:29.741948+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.03160v1","created_at":"2026-05-18T00:40:29.741948+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03160","created_at":"2026-05-18T00:40:29.741948+00:00"},{"alias_kind":"pith_short_12","alias_value":"DXA2ME5CFS5O","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"DXA2ME5CFS5ORUX6","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"DXA2ME5C","created_at":"2026-05-18T12:31:12.930513+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DXA2ME5CFS5ORUX6BKX3J4OC3U","json":"https://pith.science/pith/DXA2ME5CFS5ORUX6BKX3J4OC3U.json","graph_json":"https://pith.science/api/pith-number/DXA2ME5CFS5ORUX6BKX3J4OC3U/graph.json","events_json":"https://pith.science/api/pith-number/DXA2ME5CFS5ORUX6BKX3J4OC3U/events.json","paper":"https://pith.science/paper/DXA2ME5C"},"agent_actions":{"view_html":"https://pith.science/pith/DXA2ME5CFS5ORUX6BKX3J4OC3U","download_json":"https://pith.science/pith/DXA2ME5CFS5ORUX6BKX3J4OC3U.json","view_paper":"https://pith.science/paper/DXA2ME5C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.03160&json=true","fetch_graph":"https://pith.science/api/pith-number/DXA2ME5CFS5ORUX6BKX3J4OC3U/graph.json","fetch_events":"https://pith.science/api/pith-number/DXA2ME5CFS5ORUX6BKX3J4OC3U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DXA2ME5CFS5ORUX6BKX3J4OC3U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DXA2ME5CFS5ORUX6BKX3J4OC3U/action/storage_attestation","attest_author":"https://pith.science/pith/DXA2ME5CFS5ORUX6BKX3J4OC3U/action/author_attestation","sign_citation":"https://pith.science/pith/DXA2ME5CFS5ORUX6BKX3J4OC3U/action/citation_signature","submit_replication":"https://pith.science/pith/DXA2ME5CFS5ORUX6BKX3J4OC3U/action/replication_record"}},"created_at":"2026-05-18T00:40:29.741948+00:00","updated_at":"2026-05-18T00:40:29.741948+00:00"}