{"day":"10","year":"2011","date_published":"2011-06-10T00:00:00Z","quality_controlled":0,"date_updated":"2021-01-12T06:55:24Z","publication":"Parabolic Problems","intvolume":"        80","date_created":"2018-12-11T11:55:48Z","abstract":[{"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.","lang":"eng"}],"status":"public","page":"463 - 477","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0911.4336 "}],"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). ","extern":1,"author":[{"full_name":"Jan Maas","first_name":"Jan","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas"},{"full_name":"Van Neerven, Jan","first_name":"Jan","last_name":"Van Neerven"}],"publist_id":"4918","volume":80,"publication_status":"published","oa":1,"publisher":"Birkhäuser","citation":{"short":"J. Maas, J. Van Neerven, in:, Parabolic Problems, Birkhäuser, 2011, pp. 463–477.","apa":"Maas, J., &#38; Van Neerven, J. (2011). Gradient estimates and domain identification for analytic Ornstein-Uhlenbeck operators. In <i>Parabolic Problems</i> (Vol. 80, pp. 463–477). Birkhäuser. <a href=\"https://doi.org/10.1007/978-3-0348-0075-4_24\">https://doi.org/10.1007/978-3-0348-0075-4_24</a>","ista":"Maas J, Van Neerven J. 2011.Gradient estimates and domain identification for analytic Ornstein-Uhlenbeck operators. In: Parabolic Problems. vol. 80, 463–477.","ama":"Maas J, Van Neerven J. Gradient estimates and domain identification for analytic Ornstein-Uhlenbeck operators. In: <i>Parabolic Problems</i>. Vol 80. Birkhäuser; 2011:463-477. doi:<a href=\"https://doi.org/10.1007/978-3-0348-0075-4_24\">10.1007/978-3-0348-0075-4_24</a>","ieee":"J. Maas and J. Van Neerven, “Gradient estimates and domain identification for analytic Ornstein-Uhlenbeck operators,” in <i>Parabolic Problems</i>, vol. 80, Birkhäuser, 2011, pp. 463–477.","mla":"Maas, Jan, and Jan Van Neerven. “Gradient Estimates and Domain Identification for Analytic Ornstein-Uhlenbeck Operators.” <i>Parabolic Problems</i>, vol. 80, Birkhäuser, 2011, pp. 463–77, doi:<a href=\"https://doi.org/10.1007/978-3-0348-0075-4_24\">10.1007/978-3-0348-0075-4_24</a>.","chicago":"Maas, Jan, and Jan Van Neerven. “Gradient Estimates and Domain Identification for Analytic Ornstein-Uhlenbeck Operators.” In <i>Parabolic Problems</i>, 80:463–77. Birkhäuser, 2011. <a href=\"https://doi.org/10.1007/978-3-0348-0075-4_24\">https://doi.org/10.1007/978-3-0348-0075-4_24</a>."},"type":"book_chapter","doi":"10.1007/978-3-0348-0075-4_24","_id":"2116","title":"Gradient estimates and domain identification for analytic Ornstein-Uhlenbeck operators","month":"06"}