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We assume that these forms all have the same domain $V$. It is proved in \\cite{HO14} that if the forms have some regularity with respect to $t$ (e.g., piecewise $\\alpha$-H\\\"older continuous for some $\\alpha > 1/2$) then the above problem has maximal $L_p$--regularity"},"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":"1411.0139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-01T17:05:36Z","cross_cats_sorted":[],"title_canon_sha256":"36c14ca946138fe87d9e6046b9c45b3d1e0a5220b10c82df9267faed4a0950b4","abstract_canon_sha256":"41c34e327935063fb452a07e4f66de72ec9c0a382e6073b6f7052b9cd1d73989"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:52.457918Z","signature_b64":"mi3lwJahI04hXXgxN+DOD/ZuISwhfuaXNYRVL2nBrN5DFpY+9sJ85JU5fGcUrUsHkkT8krJOF5WFEY2ucLMYBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c56f8a7ddd79a33bb994ed08809cd1581e1245331d41000f42fdf3e401ad507","last_reissued_at":"2026-05-18T02:38:52.457543Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:52.457543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximal regularity for non-autonomous evolution equations governed by forms having less regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"El Maati Ouhabaz","submitted_at":"2014-11-01T17:05:36Z","abstract_excerpt":"We consider the maximal regularity problem for non-autonomous evolution equations  \\begin{equation}\n  \\left\\{\n  \\begin{array}{rcl}  \nu'(t) + A(t)\\,u(t) &=& f(t), \\ t \\in (0, \\tau]\n  u(0)&=&u_0.\n  \\end{array} \\right. \\end{equation} Each operator $A(t)$ is associated with a sesquilinear form $\\mathfrak{a}(t)$ on a Hilbert space $H$. We assume that these forms all have the same domain $V$. It is proved in \\cite{HO14} that if the forms have some regularity with respect to $t$ (e.g., piecewise $\\alpha$-H\\\"older continuous for some $\\alpha > 1/2$) then the above problem has maximal $L_p$--regularity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0139","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":"1411.0139","created_at":"2026-05-18T02:38:52.457601+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.0139v1","created_at":"2026-05-18T02:38:52.457601+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0139","created_at":"2026-05-18T02:38:52.457601+00:00"},{"alias_kind":"pith_short_12","alias_value":"LRLPRJ6526ND","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"LRLPRJ6526NDHO4Z","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"LRLPRJ65","created_at":"2026-05-18T12:28:38.356838+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/LRLPRJ6526NDHO4ZJ3IIQCONCW","json":"https://pith.science/pith/LRLPRJ6526NDHO4ZJ3IIQCONCW.json","graph_json":"https://pith.science/api/pith-number/LRLPRJ6526NDHO4ZJ3IIQCONCW/graph.json","events_json":"https://pith.science/api/pith-number/LRLPRJ6526NDHO4ZJ3IIQCONCW/events.json","paper":"https://pith.science/paper/LRLPRJ65"},"agent_actions":{"view_html":"https://pith.science/pith/LRLPRJ6526NDHO4ZJ3IIQCONCW","download_json":"https://pith.science/pith/LRLPRJ6526NDHO4ZJ3IIQCONCW.json","view_paper":"https://pith.science/paper/LRLPRJ65","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.0139&json=true","fetch_graph":"https://pith.science/api/pith-number/LRLPRJ6526NDHO4ZJ3IIQCONCW/graph.json","fetch_events":"https://pith.science/api/pith-number/LRLPRJ6526NDHO4ZJ3IIQCONCW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LRLPRJ6526NDHO4ZJ3IIQCONCW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LRLPRJ6526NDHO4ZJ3IIQCONCW/action/storage_attestation","attest_author":"https://pith.science/pith/LRLPRJ6526NDHO4ZJ3IIQCONCW/action/author_attestation","sign_citation":"https://pith.science/pith/LRLPRJ6526NDHO4ZJ3IIQCONCW/action/citation_signature","submit_replication":"https://pith.science/pith/LRLPRJ6526NDHO4ZJ3IIQCONCW/action/replication_record"}},"created_at":"2026-05-18T02:38:52.457601+00:00","updated_at":"2026-05-18T02:38:52.457601+00:00"}