{"paper":{"title":"Maximal regularity for non-autonomous evolution equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Bernhard Hermann Haak (IMB), E.-M. Ouhabaz (IMB)","submitted_at":"2014-02-05T19:29:20Z","abstract_excerpt":"We consider the maximal regularity problem for non-autonomous evolution equations of the form $u(t) + A(t) u(t) = f(t)$ with initial data $u(0) = u\\_0$ . Each operator $A(t)$ is associated with a sesquilinear form $a(t; *, *)$ on a Hilbert space $H$ . We assume that these forms all have the same domain and satisfy some regularity assumption with respect to t (e.g., piecewise $\\alpha$-H{\\\"o}lder continuous for some $\\alpha\\textgreater{} 1/2$). We prove maximal Lp-regularity for all initial values in the real-interpolation space $(H, D(A(0)))\\_{1/p,p}$ . The particular case where $p = 2$ improve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1136","kind":"arxiv","version":3},"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"}