{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HMPOEW4KWGFY5GPBFHA5IGMMQD","short_pith_number":"pith:HMPOEW4K","schema_version":"1.0","canonical_sha256":"3b1ee25b8ab18b8e99e129c1d4198c80c4899d181daf7441a23a71a67b7a0865","source":{"kind":"arxiv","id":"1709.06117","version":1},"attestation_state":"computed","paper":{"title":"On the boundary conditions in estimating $\\nabla \\omega$ by div $\\omega$ and curl $\\omega.$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dhanya Rajendran, Gyula Csat\\'o, Olivier Kneuss","submitted_at":"2017-09-18T18:32:21Z","abstract_excerpt":"In this paper we study under what boundary conditions the inequality $$\\|\\nabla\\omega\\|_{L^2(\\Omega)}^2\\leq C\\left(\\|{\\rm curl}\\omega\\|_{L^2(\\Omega)}^2+ \\|{\\rm div}\\omega\\|_{L^2(\\Omega)}^2+\\|\\omega\\|_{L^2(\\Omega)}^2\\right) $$ holds true. It is known that such an estimate holds if either the tangential or normal component of $\\omega$ vanishes on the boundary $\\partial\\omega.$ We show that the vanishing tangential component condition is a special case of a more general one. In two dimensions we give an interpolation result between these two classical boundary conditions."},"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":"1709.06117","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-18T18:32:21Z","cross_cats_sorted":[],"title_canon_sha256":"ad68e4c11103054dbdd5fa0a0e4c5e7513c62affdf63ef81a6f57d3edbaa0f52","abstract_canon_sha256":"e9f89a9bc9aedbf6bdb07a4c3618d690c22c0633ac6292a88f811fce9e0c1ff6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:54.374632Z","signature_b64":"OdIvXWf6atsGfHTgRi4B34pdOVFM4IHNH3oXOWaMtlVLpHeHCYlQJMKMECW29zJ/KuQUgxUMPgJ/fcAMYB25Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b1ee25b8ab18b8e99e129c1d4198c80c4899d181daf7441a23a71a67b7a0865","last_reissued_at":"2026-05-18T00:34:54.373972Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:54.373972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the boundary conditions in estimating $\\nabla \\omega$ by div $\\omega$ and curl $\\omega.$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dhanya Rajendran, Gyula Csat\\'o, Olivier Kneuss","submitted_at":"2017-09-18T18:32:21Z","abstract_excerpt":"In this paper we study under what boundary conditions the inequality $$\\|\\nabla\\omega\\|_{L^2(\\Omega)}^2\\leq C\\left(\\|{\\rm curl}\\omega\\|_{L^2(\\Omega)}^2+ \\|{\\rm div}\\omega\\|_{L^2(\\Omega)}^2+\\|\\omega\\|_{L^2(\\Omega)}^2\\right) $$ holds true. It is known that such an estimate holds if either the tangential or normal component of $\\omega$ vanishes on the boundary $\\partial\\omega.$ We show that the vanishing tangential component condition is a special case of a more general one. In two dimensions we give an interpolation result between these two classical boundary conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06117","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":"1709.06117","created_at":"2026-05-18T00:34:54.374067+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.06117v1","created_at":"2026-05-18T00:34:54.374067+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06117","created_at":"2026-05-18T00:34:54.374067+00:00"},{"alias_kind":"pith_short_12","alias_value":"HMPOEW4KWGFY","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HMPOEW4KWGFY5GPB","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HMPOEW4K","created_at":"2026-05-18T12:31:18.294218+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/HMPOEW4KWGFY5GPBFHA5IGMMQD","json":"https://pith.science/pith/HMPOEW4KWGFY5GPBFHA5IGMMQD.json","graph_json":"https://pith.science/api/pith-number/HMPOEW4KWGFY5GPBFHA5IGMMQD/graph.json","events_json":"https://pith.science/api/pith-number/HMPOEW4KWGFY5GPBFHA5IGMMQD/events.json","paper":"https://pith.science/paper/HMPOEW4K"},"agent_actions":{"view_html":"https://pith.science/pith/HMPOEW4KWGFY5GPBFHA5IGMMQD","download_json":"https://pith.science/pith/HMPOEW4KWGFY5GPBFHA5IGMMQD.json","view_paper":"https://pith.science/paper/HMPOEW4K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.06117&json=true","fetch_graph":"https://pith.science/api/pith-number/HMPOEW4KWGFY5GPBFHA5IGMMQD/graph.json","fetch_events":"https://pith.science/api/pith-number/HMPOEW4KWGFY5GPBFHA5IGMMQD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HMPOEW4KWGFY5GPBFHA5IGMMQD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HMPOEW4KWGFY5GPBFHA5IGMMQD/action/storage_attestation","attest_author":"https://pith.science/pith/HMPOEW4KWGFY5GPBFHA5IGMMQD/action/author_attestation","sign_citation":"https://pith.science/pith/HMPOEW4KWGFY5GPBFHA5IGMMQD/action/citation_signature","submit_replication":"https://pith.science/pith/HMPOEW4KWGFY5GPBFHA5IGMMQD/action/replication_record"}},"created_at":"2026-05-18T00:34:54.374067+00:00","updated_at":"2026-05-18T00:34:54.374067+00:00"}