Dirichlet spaces on H-convex sets in Wiener space

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.

18 pages, 1 figure. Erratum has been added, which was accepted for publication in Bull. Sci. Math

References in corpus (3)

• Sets of finite perimeter and the Hausdorff-Gauss measure on the Wiener space
• Analysis on Wiener Space and Applications
• Dirichlet spaces on H-convex sets in Wiener space

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