--- _id: '2116' abstract: - lang: eng text: 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. 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). ' author: - first_name: Jan full_name: Jan Maas id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Jan full_name: Van Neerven, Jan last_name: Van Neerven citation: ama: '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' apa: 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 chicago: 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. ieee: 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. ista: 'Maas J, Van Neerven J. 2011.Gradient estimates and domain identification for analytic Ornstein-Uhlenbeck operators. In: Parabolic Problems. vol. 80, 463–477.' mla: 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. short: J. Maas, J. Van Neerven, in:, Parabolic Problems, Birkhäuser, 2011, pp. 463–477. date_created: 2018-12-11T11:55:48Z date_published: 2011-06-10T00:00:00Z date_updated: 2021-01-12T06:55:24Z day: '10' doi: 10.1007/978-3-0348-0075-4_24 extern: 1 intvolume: ' 80' main_file_link: - open_access: '1' url: 'http://arxiv.org/abs/0911.4336 ' month: '06' oa: 1 page: 463 - 477 publication: Parabolic Problems publication_status: published publisher: Birkhäuser publist_id: '4918' quality_controlled: 0 status: public title: Gradient estimates and domain identification for analytic Ornstein-Uhlenbeck operators type: book_chapter volume: 80 year: '2011' ...