{"paper":{"title":"Maximal Regularity for Evolution Equations Governed by Non-Autonomous Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dominik Dier, El Maati Ouhabaz (IMB), Hafida Laasri, Wolfgang Arendt","submitted_at":"2013-03-05T20:32:21Z","abstract_excerpt":"\\begin{abstract}\\label{abstract} We consider a non-autonomous evolutionary problem \\[ \\dot{u} (t)+\\A(t)u(t)=f(t), \\quad u(0)=u_0 \\] where the operator $\\A(t):V\\to V^\\prime$ is associated with a form $\\fra(t,.,.):V\\times V \\to \\R$ and $u_0\\in V$. Our main concern is to prove well-posedness with maximal regularity which means the following. Given a Hilbert space $H$ such that $V$ is continuously and densely embedded into $H$ and given $f\\in L^2(0,T;H)$ we are interested in solutions $u \\in H^1(0,T;H)\\cap L^2(0,T;V)$. We do prove well-posedness in this sense whenever the form is piecewise Lipschi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1166","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"}