The Ornstein-Uhlenbeck semigroup in exterior domains

Ian Wood; Matthias Geissert; Horst Heck; Matthias Hieber

doi:10.1007/s00013-005-1400-4

The Ornstein-Uhlenbeck semigroup in exterior domains

Ian Wood, Matthias Geissert, Horst Heck, Matthias Hieber

Department of Physics

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

Let Ω be an exterior domain in It is shown that Ornstein-Uhlenbeck operators L generate C0-semigroups on Lp(Ω) for p ∈ (1, ∞) provided ∂Ω is smooth. The method presented also allows to determine the domain D(L) of L and to prove Lp − Lq smoothing properties of etL. If ∂Ω is only Lipschitz, results of this type are shown to be true for p close to 2.

Original language	English
Pages (from-to)	554-562
Number of pages	9
Journal	Archiv der Mathematik
Volume	85
Issue number	6
DOIs	https://doi.org/10.1007/s00013-005-1400-4
Publication status	Published - Dec 2005

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abstract = "Let Ω be an exterior domain in It is shown that Ornstein-Uhlenbeck operators L generate C0-semigroups on Lp(Ω) for p ∈ (1, ∞) provided ∂Ω is smooth. The method presented also allows to determine the domain D(L) of L and to prove Lp − Lq smoothing properties of etL. If ∂Ω is only Lipschitz, results of this type are shown to be true for p close to 2.",

author = "Ian Wood and Matthias Geissert and Horst Heck and Matthias Hieber",

note = "Wood, Ian; Geissert, M.; Heck, H.; Hieber, M., (2005) 'The Ornstein-Uhlenbeck semigroup in exterior domains', Archiv der Mathematik 86 pp.554-562 RAE2008",

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AU - Geissert, Matthias

AU - Heck, Horst

AU - Hieber, Matthias

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PY - 2005/12

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N2 - Let Ω be an exterior domain in It is shown that Ornstein-Uhlenbeck operators L generate C0-semigroups on Lp(Ω) for p ∈ (1, ∞) provided ∂Ω is smooth. The method presented also allows to determine the domain D(L) of L and to prove Lp − Lq smoothing properties of etL. If ∂Ω is only Lipschitz, results of this type are shown to be true for p close to 2.

AB - Let Ω be an exterior domain in It is shown that Ornstein-Uhlenbeck operators L generate C0-semigroups on Lp(Ω) for p ∈ (1, ∞) provided ∂Ω is smooth. The method presented also allows to determine the domain D(L) of L and to prove Lp − Lq smoothing properties of etL. If ∂Ω is only Lipschitz, results of this type are shown to be true for p close to 2.

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DO - 10.1007/s00013-005-1400-4

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SP - 554

EP - 562

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 6

ER -

The Ornstein-Uhlenbeck semigroup in exterior domains

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