{"paper":{"title":"Non-Autonomous Forms and Invariance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dominik Dier","submitted_at":"2016-09-13T14:28:35Z","abstract_excerpt":"We generalize the Beurling--Deny--Ouhabaz criterion for parabolic evolution equations governed by forms to the non-autonomous, non-homogeneous and semilinear case. Let $V, H$ are Hilbert spaces such that $V$ is continuously and densely embedded in $H$ and let $\\mathcal{A}(t)\\colon V\\to V^\\prime$ be the operator associated with a bounded $H$-elliptic form $\\mathfrak{a}(t,.,.)\\colon V\\times V \\to \\mathbb{C}$ for all $t \\in [0,T]$. Suppose $\\mathcal{C} \\subset H$ is closed and convex and $P \\colon H \\to H$ the orthogonal projection onto $\\mathcal{C}$. Given $f \\in L^2(0,T;V')$ and $u_0\\in \\mathca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03857","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"}