The domain of the Ornstein-Uhlenbeck operator on an $L^p$-space with invariant measure

By Giorgio Metafune, Jan Prüss, Abdelaziz Rhandi, Roland Schnaubelt. 2002

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View Paper: https://www.semanticscholar.org/paper/3b4b15c41101cb0624a44d93c22b6714ab560184

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Citations in the corpus

Maximal $L^p$-regularity for stochastic evolution equations (2011, background): “. Necessary and suﬃcient conditions for the validity of the analogous identiﬁcation in the non-symmetric and inﬁnite-dimensionsional case were obtained in [58]; special cases were obtained earlier in [16, 60, 80]. 3.2. Maximal Lp-regularity. Let −Abe the generator of a bounded analytic C0-semigroup ”
The Navier-Stokes Equations in ℝn with Linearly Growing Initial Data (2005, methodology): “Then the following result on the Ornstein-Uhlenbeck semigroup was proved by Metafune ,P allara &P riola [25] and by Metafune ,P russ ,R handi & Schnaubelt [ 26 ].”
Estimates of the derivatives for parabolic operators with unbounded coefficients (2005, background): “There are just a few results in the particular case when the drift term is a gradient (see [16]) or A is an Ornstein-Uhlenbeck operator (see [15]).”
Gaussian Measures on Separable Hilbert Spaces and Applications (2004, background): “Recently, this result was extended to p ∈ (1,∞) (see [25] or [26]).”
Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift (2011, unknown): “5) The following extension to Lp(µ), p>1, can be found in Section 3 of [CG02] (see also [CG01] and [MV11]; a ﬁnite dimensional result analogous to this for non-symmetric OU operators was proved in [MPRS02]). Theorem 3. Let λ>0, f∈ Lp(H,µ) and let ϕ∈ D(Lp) be the solution of the equation λϕ−Lp ”