The Dirichlet-to-Neumann operator on rough domains

Arendt, W; ter Elst, Antonius

dc.contributor.author	Arendt, W	en
dc.contributor.author	ter Elst, Antonius	en
dc.date.accessioned	2012-03-08T21:10:30Z	en
dc.date.issued	2011	en
dc.identifier.citation	Journal of Differential Equations 251(8):2100-2124 15 Oct 2011	en
dc.identifier.issn	0022-0396	en
dc.identifier.uri	http://hdl.handle.net/2292/13555	en
dc.description.abstract	We consider a bounded connected open set Ω⊂RdΩ⊂Rd whose boundary Γ has a finite (d−1)(d−1)-dimensional Hausdorff measure. Then we define the Dirichlet-to-Neumann operator D0D0 on L2(Γ)L2(Γ) by form methods. The operator −D0−D0 is self-adjoint and generates a contractive C0C0-semigroup S=(St)t>0S=(St)t>0 on L2(Γ)L2(Γ). We show that the asymptotic behaviour of StSt as t→∞t→∞ is related to properties of the trace of functions in H1(Ω)H1(Ω) which Ω may or may not have.	en
dc.relation.ispartofseries	Journal of Differential Equations	en
dc.rights	Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Details obtained from: http://www.sherpa.ac.uk/romeo/issn/0022-0396/	en
dc.rights.uri	https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm	en
dc.title	The Dirichlet-to-Neumann operator on rough domains	en
dc.type	Journal Article	en
dc.identifier.doi	10.1016/j.jde.2011.06.017	en
pubs.issue	8	en
pubs.begin-page	2100	en
pubs.volume	251	en
dc.rights.holder	Copyright: ACADEMIC PRESS INC ELSEVIER SCIENCE	en
pubs.end-page	2124	en
dc.rights.accessrights	http://purl.org/eprint/accessRights/RestrictedAccess	en
pubs.subtype	Article	en
pubs.elements-id	225037	en
pubs.org-id	Science	en
pubs.org-id	Mathematics	en
dc.identifier.eissn	1090-2732	en
pubs.record-created-at-source-date	2015-06-23	en