2020
DOI: 10.1142/s0219025720500046
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Domains of elliptic operators on sets in Wiener space

Abstract: Let [Formula: see text] be a separable Banach space endowed with a non-degenerate centered Gaussian measure [Formula: see text]. The associated Cameron–Martin space is denoted by [Formula: see text]. Consider two sufficiently regular convex functions [Formula: see text] and [Formula: see text]. We let [Formula: see text] and [Formula: see text]. In this paper, we study the domain of the self-adjoint operator associated with the quadratic form [Formula: see text] and we give sharp embedding results for it. In p… Show more

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Cited by 15 publications
(15 citation statements)
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“…Here S(t) is the Ornstein-Uhlenbeck semigroup in (1). To conclude we prove that condition (40) is equivalent to (39).…”
Section: (X))dγ (Y)dν(x)mentioning
confidence: 77%
See 2 more Smart Citations
“…Here S(t) is the Ornstein-Uhlenbeck semigroup in (1). To conclude we prove that condition (40) is equivalent to (39).…”
Section: (X))dγ (Y)dν(x)mentioning
confidence: 77%
“…) and the space D 1, p (X, ν), p > 1 can be defined as the domain of its closure (still denoted by D H ). In a similar way we may define D 2, p (X, ν), p ∈ (1, ∞) (for more details see [1,9,16]). The Gaussian integration by parts formula…”
Section: Hypotheses 1 (I) Q ∈ L(x ) Is a Self-adjoint And Non-negative Operator Withmentioning
confidence: 99%
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“…In Section 5 we will restrict to the case where F is a gradient perturbation, namely it has a potential. In this case the invariant measure ν is a weighted Gaussian measure and it is possible to associate a quadratic form Q 2 to N 2 , see for example [2,3,9,10,20,25,26,27,30,31,40]. Under some additional hypotheses (Hypotheses 5.5) we will define the Sobolev space W 1,2 C (X, ν), and we will show that there exists a quadratic form Q 2 on W 1,2 C (X, ν) such that…”
Section: Introductionmentioning
confidence: 99%
“…After, proceeding as in [24, Section 3], we will consider a suitable Sobolev space W 1,2 C (X, ν) of the functions u : O → R such that their null extension u belongs to W 1,2 C (X, ν), and the quadratic form…”
Section: Introductionmentioning
confidence: 99%