25 research outputs found
Invariant Measures and Maximal L^2 Regularity for Nonautonomous Ornstein-Uhlenbeck Equations
We characterize the domain of the realization of the linear parabolic
operator Gu := u_t + L(t)u (where, for each real t, L(t) is an
Ornstein-Uhlenbeck operator), in L^2 spaces with respect to a suitable measure,
that is invariant for the associated evolution semigroup. As a byproduct, we
obtain optimal L^2 regularity results for evolution equations with
time-depending Ornstein-Uhlenbeck operators
--regularity for parabolic operators with unbounded time--dependent coefficients
We establish the maximal regularity for nonautonomous Ornstein-Uhlenbeck
operators in -spaces with respect to a family of invariant measures, where
. This result follows from the maximal -regularity for a
class of elliptic operators with unbounded, time-dependent drift coefficients
and potentials acting on with Lebesgue measure
ASYMPTOTIC BEHAVIOR AND HYPERCONTRACTIVITY IN NONAUTONOMOUS ORNSTEIN-UHLENBECK EQUATIONS
Abstract. In this paper we investigate a class of nonautonomous linear parabolic problems with time-depending Ornstein-Uhlenbeck operators. We study the asymptotic behavior of the associated evolution operator and evolution semigroup in the periodic and non-periodic situation. Moreover, we show that the associated evolution operator is hypercontractive. 1