{"paper":{"title":"Maximal $L^2$ regularity for Dirichlet problems in Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandra Lunardi, Giuseppe Da Prato","submitted_at":"2012-01-18T15:03:04Z","abstract_excerpt":"We consider the Dirichlet problem $\\lambda U - {\\mathcal{L}}U= F$ in \\mathcal{O}, U=0 on $\\partial \\mathcal{O}$. Here $F\\in L^2(\\mathcal{O}, \\mu)$ where $\\mu$ is a nondegenerate centered Gaussian measure in a Hilbert space $X$, $\\mathcal{L}$ is an Ornstein-Uhlenbeck operator, and $\\mathcal{O}$ is an open set in $X$ with good boundary. We address the problem whether the weak solution $U$ belongs to the Sobolev space $W^{2,2}(\\mathcal{O}, \\mu)$. It is well known that the question has positive answer if $\\mathcal{O} = X$; if $\\mathcal{O} \\neq X$ we give a sufficient condition in terms of geometri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3809","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"}