{"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 $u \\in H^1(0,T;H)$. This property of maximal re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2884","kind":"arxiv","version":2},"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"}