{"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"}