{"paper":{"title":"Traces of Sobolev functions on regular surfaces in infinite dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandra Lunardi, Pietro Celada","submitted_at":"2013-02-09T07:52:55Z","abstract_excerpt":"In a Banach space $X$ endowed with a nondegenerate Gaussian measure, we consider Sobolev spaces of real functions defined in a sublevel set $O= \\{x\\in X:\\;G(x) <0\\}$ of a Sobolev nondegenerate function $G:X\\mapsto \\R$. We define the traces at $G^{-1}(0)$ of the elements of $W^{1,p}(O, \\mu)$ for $p>1$, as elements of $L^1(G^{-1}(0), \\rho)$ where $\\rho$ is the surface measure of Feyel and de La Pradelle. The range of the trace operator is contained in $L^q(G^{-1}(0), \\rho)$ for $1\\leq q<p$ and even in $L^p(G^{-1}(0), \\rho)$ under further assumptions. If $O$ is a suitable halfspace, the range is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2204","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"}