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Given $f \\in L^2(0,T;H)$, $u_0\\in V$ there exists always a unique solution $u \\in MR(V,V'):= L^2(0,T;V) \\cap H^1(0,T;V')$. The purpose of this article is to investigate when $u \\in H^1(0,T;H)$. This property of maximal re"},"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":"1406.2884","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-11T12:30:55Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"81c06c14312bd35d6c5defbc0791037577d2bb4757a9ed2cff21c268a0180848","abstract_canon_sha256":"ab570439a81892ff4f03b0cca6a4ed903955be0b9d43bfe7cb05a73c5a96852f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:53.310006Z","signature_b64":"fhVCchRyX5zBr3qZpeO4pC9yYAAPmI9VvFwLCw6365ssonZ46xP3rcyyHQXYi/kUg4PzO7wzcYsFtxyqrUj/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"faf87c1a682ac4559f6087c62b8a9883ecf7dc465a0ef8e2af7a04c4aae51d29","last_reissued_at":"2026-05-18T02:49:53.309584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:53.309584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-Autonomous Maximal Regularity for Forms of Bounded Variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Dominik Dier","submitted_at":"2014-06-11T12:30:55Z","abstract_excerpt":"We consider a non-autonomous evolutionary problem \\[ u' (t)+\\mathcal A (t)u(t)=f(t), \\quad u(0)=u_0, \\] where $V, H$ are Hilbert spaces such that $V$ is continuously and densely embedded in $H$ and the operator $\\mathcal A (t)\\colon V\\to V^\\prime$ is associated with a coercive, bounded, symmetric form $\\mathfrak{a}(t,.,.)\\colon V\\times V \\to \\mathbb{C}$ for all $t \\in [0,T]$. Given $f \\in L^2(0,T;H)$, $u_0\\in V$ there exists always a unique solution $u \\in MR(V,V'):= L^2(0,T;V) \\cap H^1(0,T;V')$. The purpose of this article is to investigate when $u \\in H^1(0,T;H)$. 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