Gradient estimates and domain identification for analytic Ornstein-Uhlenbeck operators

J. Maas, J. Van Neerven, in:, Parabolic Problems, Birkhäuser, 2011, pp. 463–477.


Book Chapter | Published
Author
Maas, JanIST Austria ; Van Neerven, Jan
Abstract
Let P be the Ornstein-Uhlenbeck semigroup associated with the stochastic Cauchy problem dU(t)=AU(t)dt+dWH(t), where A is the generator of a C 0-semigroup S on a Banach space E, H is a Hilbert subspace of E, and W H is an H-cylindrical Brownian motion. Assuming that S restricts to a C 0-semigroup on H, we obtain L p -bounds for D H P(t). We show that if P is analytic, then the invariance assumption is fulfilled. As an application we determine the L p -domain of the generator of P explicitly in the case where S restricts to a C 0-semigroup on H which is similar to an analytic contraction semigroup. The results are applied to the 1D stochastic heat equation driven by additive space-time white noise.
Publishing Year
Date Published
2011-06-10
Book Title
Parabolic Problems
Acknowledgement
The authors are supported by VIDI subsidy 639.032.201 (JM) and VICI subsidy 639.033.604 (JvN) of the Netherlands Organisation for Scientific Research (NWO).
Volume
80
Page
463 - 477
IST-REx-ID

Cite this

Maas J, Van Neerven J. Gradient estimates and domain identification for analytic Ornstein-Uhlenbeck operators. In: Parabolic Problems. Vol 80. Birkhäuser; 2011:463-477. doi:10.1007/978-3-0348-0075-4_24
Maas, J., & Van Neerven, J. (2011). Gradient estimates and domain identification for analytic Ornstein-Uhlenbeck operators. In Parabolic Problems (Vol. 80, pp. 463–477). Birkhäuser. https://doi.org/10.1007/978-3-0348-0075-4_24
Maas, Jan, and Jan Van Neerven. “Gradient Estimates and Domain Identification for Analytic Ornstein-Uhlenbeck Operators.” In Parabolic Problems, 80:463–77. Birkhäuser, 2011. https://doi.org/10.1007/978-3-0348-0075-4_24.
J. Maas and J. Van Neerven, “Gradient estimates and domain identification for analytic Ornstein-Uhlenbeck operators,” in Parabolic Problems, vol. 80, Birkhäuser, 2011, pp. 463–477.
Maas J, Van Neerven J. 2011. Gradient estimates and domain identification for analytic Ornstein-Uhlenbeck operators. Parabolic Problems. vol. 80. 463–477.
Maas, Jan, and Jan Van Neerven. “Gradient Estimates and Domain Identification for Analytic Ornstein-Uhlenbeck Operators.” Parabolic Problems, vol. 80, Birkhäuser, 2011, pp. 463–77, doi:10.1007/978-3-0348-0075-4_24.
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