On functions of bounded variation on convex domains in Hilbert spaces

We study functions of bounded variation (and sets of finite perimeter) on a convex open set Ω ⊆ X , X being an infinite-dimensional separable real Hilbert space. We relate the total variation of such functions, defined through an integration by parts formula, to the short-time behaviour of the semig...

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Bibliographic Details
Published inJournal of evolution equations Vol. 21; no. 3; pp. 3449 - 3475
Main Authors Angiuli, Luciana, Ferrari, Simone, Pallara, Diego
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.09.2021
Springer Nature B.V
Subjects
Analysis
Hilbert space
Mathematics
Mathematics and Statistics
Operators (mathematics)
Perturbation
Infinite-dimensional analysis
Functions of bounded variation
Semigroups of bounded operators
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Summary:We study functions of bounded variation (and sets of finite perimeter) on a convex open set Ω ⊆ X , X being an infinite-dimensional separable real Hilbert space. We relate the total variation of such functions, defined through an integration by parts formula, to the short-time behaviour of the semigroup associated with a perturbation of the Ornstein–Uhlenbeck operator.
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-021-00680-8