{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:3NGPRSYZ3XRQ74OYJYXWWQQHLD","short_pith_number":"pith:3NGPRSYZ","schema_version":"1.0","canonical_sha256":"db4cf8cb19dde30ff1d84e2f6b420758c96bc80b48d9c7c6a246c425b75afe04","source":{"kind":"arxiv","id":"1709.02880","version":1},"attestation_state":"computed","paper":{"title":"Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in $\\text{int}(K^{lc})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angkana R\\\"uland, Barbara Zwicknagl, Christian Zillinger","submitted_at":"2017-09-08T23:36:45Z","abstract_excerpt":"In this article we continue our study of higher Sobolev regularity of flexible convex integration solutions to differential inclusions arising from applications in materials sciences. We present a general framework yielding higher Sobolev regularity for Dirichlet problems with affine data in $\\text{int}(K^{lc})$. This allows us to simultaneously deal with linear and nonlinear differential inclusion problems. We show that the derived higher integrability and differentiability exponent has a lower bound, which is independent of the position of the Dirichlet boundary data in $\\text{int}(K^{lc})$."},"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":"1709.02880","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-08T23:36:45Z","cross_cats_sorted":[],"title_canon_sha256":"e43f99308cfd9f9123261c9321e4a3c9bbd3572965140644b0fc9ddb2970c626","abstract_canon_sha256":"b0e48af14e3246b0a99c43efc899add1cb9d8f9594ec30e0a7c3fab25acab6c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:40.258929Z","signature_b64":"USUfI8R0iuUIgCX5l1XqrNMhy7uNg2A4s8BeaMzfBVDgBrmzH9dXhuu5sqyvVnNanwPDuEOVE9bhM0t6sTJMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db4cf8cb19dde30ff1d84e2f6b420758c96bc80b48d9c7c6a246c425b75afe04","last_reissued_at":"2026-05-18T00:35:40.258193Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:40.258193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in $\\text{int}(K^{lc})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angkana R\\\"uland, Barbara Zwicknagl, Christian Zillinger","submitted_at":"2017-09-08T23:36:45Z","abstract_excerpt":"In this article we continue our study of higher Sobolev regularity of flexible convex integration solutions to differential inclusions arising from applications in materials sciences. We present a general framework yielding higher Sobolev regularity for Dirichlet problems with affine data in $\\text{int}(K^{lc})$. This allows us to simultaneously deal with linear and nonlinear differential inclusion problems. We show that the derived higher integrability and differentiability exponent has a lower bound, which is independent of the position of the Dirichlet boundary data in $\\text{int}(K^{lc})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02880","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":"1709.02880","created_at":"2026-05-18T00:35:40.258306+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.02880v1","created_at":"2026-05-18T00:35:40.258306+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02880","created_at":"2026-05-18T00:35:40.258306+00:00"},{"alias_kind":"pith_short_12","alias_value":"3NGPRSYZ3XRQ","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_16","alias_value":"3NGPRSYZ3XRQ74OY","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_8","alias_value":"3NGPRSYZ","created_at":"2026-05-18T12:30:58.224056+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/3NGPRSYZ3XRQ74OYJYXWWQQHLD","json":"https://pith.science/pith/3NGPRSYZ3XRQ74OYJYXWWQQHLD.json","graph_json":"https://pith.science/api/pith-number/3NGPRSYZ3XRQ74OYJYXWWQQHLD/graph.json","events_json":"https://pith.science/api/pith-number/3NGPRSYZ3XRQ74OYJYXWWQQHLD/events.json","paper":"https://pith.science/paper/3NGPRSYZ"},"agent_actions":{"view_html":"https://pith.science/pith/3NGPRSYZ3XRQ74OYJYXWWQQHLD","download_json":"https://pith.science/pith/3NGPRSYZ3XRQ74OYJYXWWQQHLD.json","view_paper":"https://pith.science/paper/3NGPRSYZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.02880&json=true","fetch_graph":"https://pith.science/api/pith-number/3NGPRSYZ3XRQ74OYJYXWWQQHLD/graph.json","fetch_events":"https://pith.science/api/pith-number/3NGPRSYZ3XRQ74OYJYXWWQQHLD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3NGPRSYZ3XRQ74OYJYXWWQQHLD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3NGPRSYZ3XRQ74OYJYXWWQQHLD/action/storage_attestation","attest_author":"https://pith.science/pith/3NGPRSYZ3XRQ74OYJYXWWQQHLD/action/author_attestation","sign_citation":"https://pith.science/pith/3NGPRSYZ3XRQ74OYJYXWWQQHLD/action/citation_signature","submit_replication":"https://pith.science/pith/3NGPRSYZ3XRQ74OYJYXWWQQHLD/action/replication_record"}},"created_at":"2026-05-18T00:35:40.258306+00:00","updated_at":"2026-05-18T00:35:40.258306+00:00"}