Wood, Ian
(2009)
*The Ornstein-Uhlenbeck Semigroup in Bounded and Exterior Lipschitz Domains.*
In: Janas, Jan and Kurasov, Pavel and Naboko, Serguei and Laptev, Ari and Stolz, Gunter, eds.
Methods of Spectral Analysis in Mathematical Physics.
Operator Theory: Advances and Applications, 186
.
Birkhaeuser, Basel, pp. 415-435.
ISBN 9783764387549.
(The full text of this publication is not available from this repository)

The full text of this publication is not available from this repository. (Contact us about this Publication) | |

Official URL http://dx.doi.org/10.1007/978-3-7643-8755-6_21 |

## Abstract

We consider bounded Lipschitz domains Ω in ℝ n . It is shown that the Dirichlet-Laplacian generates an analytic C 0-semigroup on L p (Ω) for p in an interval around 2 and that the corresponding Cauchy problem has the maximal L q -regularity property. We then prove that for bounded or exterior Lipschitz domains Ornstein-Uhlenbeck operators A generate C 0-semigroups in the same p-interval. The method, also allows to determine the domain D(A) of A and, if Ω satisfies an outer ball condition, allows to show L p -L q -smoothing properties of the semigroups.

Item Type: | Book section |
---|---|

Subjects: | Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations |

Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science |

Depositing User: | Ian Wood |

Date Deposited: | 09 Apr 2010 10:56 |

Last Modified: | 28 Jul 2014 08:09 |

Resource URI: | http://kar.kent.ac.uk/id/eprint/23941 (The current URI for this page, for reference purposes) |

- Export to:
- RefWorks
- EPrints3 XML
- CSV

- Depositors only (login required):