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Journal of the London Mathematical Society Advance Access originally published online on April 2, 2008
Journal of the London Mathematical Society 2008 77(3):719-740; doi:10.1112/jlms/jdn009
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© 2008 London Mathematical Society

Invariant measures and maximal L2 regularity for nonautonomous Ornstein–Uhlenbeck equations

Matthias Geissert

FB Mathematik
Schlossgartenstr. 7
TU Darmstadt
64289 Darmstadt
Germany

Alessandra Lunardi

Dipartimento di Matematica
Parco Area delle Scienze 53/A
43100 Parma
Italy
alessandra.lunardi@unipr.it

We characterize the domain of the realizations of a linear parabolic operator G defined in L2 spaces with respect to a suitable measure that is invariant for the associated evolution semigroup. As a byproduct, we obtain optimal L2 regularity results for evolution equations with time-dependant Ornstein–Uhlenbeck operators.

The first author was partially supported by the MIUR – PRIN 2004 Research project ‘Kolmogorov Equations’.

2000 Mathematics Subject Classification 47D06, 47F05, 35B65.

Received June 14, 2007; revised October 17, 2007; published online April 2, 2008.


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