{"paper":{"title":"Evolution Equations governed by Lipschitz Continuous Non-autonomous Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ahmed Sani, Hafida Laasri","submitted_at":"2014-11-14T12:25:58Z","abstract_excerpt":"We prove $L^2$-maximal regularity of linear non-autonomous evolutionary Cauchy problem \\begin{equation}\\label{eq00}\\nonumber \\dot{u} (t)+A(t)u(t)=f(t) \\hbox{ for }\\ \\hbox{a.e. t}\\in [0,T],\\quad u(0)=u_0, \\end{equation} where the operator $A(t)$ arises from a time dependent sesquilinear form $a(t,.,.)$ on a Hilbert space $H$ with constant domain $V.$ We prove the maximal regularity in $H$ when these forms are time Lipschitz continuous. We proceed by approximating the problem using the frozen coefficient method developed in \\cite{ELKELA11}, \\cite{ELLA13} and \\cite{LH}. As a consequence, we obtai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3882","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"}