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arXiv · 1105.3300

Dirichlet spaces on H-convex sets in Wiener space

Masanori Hino
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Abstract

We consider the $(1,2)$-Sobolev space $W^{1,2}(U)$ on subsets $U$ in an abstract Wiener space, which is regarded as a canonical Dirichlet space on $U$. We prove that $W^{1,2}(U)$ has smooth cylindrical functions as a dense subset if $U$ is $H$-convex and $H$-open. For the proof, the relations between $H$-notions and quasi-notions are also studied.

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BibTeXRIS

Masanori Hino. 2012-12-27. Dirichlet spaces on H-convex sets in Wiener space. https://doi.org/10.1016/j.bulsci.2011.07.008

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