---
_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'
...