We study the basic theory of BV functions in a Hilbert space X endowed with a (not necessarily Gaussian) probability measure ν. We present necessary and sufficient conditions in order that a function u∈ Lp(X, ν) is of bounded variation. We also discuss the De Giorgi approach to BV functions through the behavior as t→ 0 of ∫X‖∇T(t)u‖dν, for a smoothing semigroup T(t). Particular attention is devoted to the case where u is the indicator function of a sublevel set {x:g(x)
BV functions in Hilbert spaces / Da Prato, G.; Lunardi, A.. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - (2020). [10.1007/s00208-020-02037-x]
BV functions in Hilbert spaces
Lunardi A.
2020-01-01
Abstract
We study the basic theory of BV functions in a Hilbert space X endowed with a (not necessarily Gaussian) probability measure ν. We present necessary and sufficient conditions in order that a function u∈ Lp(X, ν) is of bounded variation. We also discuss the De Giorgi approach to BV functions through the behavior as t→ 0 of ∫X‖∇T(t)u‖dν, for a smoothing semigroup T(t). Particular attention is devoted to the case where u is the indicator function of a sublevel set {x:g(x)File in questo prodotto:
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