TY - JOUR
T1 - The Ornstein-Uhlenbeck semigroup in exterior domains
AU - Geissert, M.
AU - Heck, H.
AU - Hieber, Matthias Georg
AU - Wood, I.
PY - 2005/12
Y1 - 2005/12
N2 - Let Ω be an exterior domain in ℝn. It is shown that Ornstein-Uhlenbeck operators L generate C0-semigroups on L p (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 ℝn. It is shown that Ornstein-Uhlenbeck operators L generate C0-semigroups on L p (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.
UR - http://www.scopus.com/inward/record.url?scp=29844438659&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=29844438659&partnerID=8YFLogxK
U2 - 10.1007/s00013-005-1400-4
DO - 10.1007/s00013-005-1400-4
M3 - Article
AN - SCOPUS:29844438659
VL - 85
SP - 554
EP - 562
JO - Archiv der Mathematik
JF - Archiv der Mathematik
SN - 0003-889X
IS - 6
ER -