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Sobolev spaces on non-smooth domains and Dirichlet forms related to subordinate reflecting diffusions


Farkas, Walter; Jacob, Niels (2001). Sobolev spaces on non-smooth domains and Dirichlet forms related to subordinate reflecting diffusions. Mathematische Nachrichten, 224(1):75-104.

Abstract

Let Ω be a bounded domain with fractal boundary, for instance von Koch's snowflake domain. First we determine the range and the kernel of the trace on ∂Ω of Sobolev spaces of fractional order defined on Ω. This extends some earlier results of H. Wallin and J. Marschall Secondly we apply these results in studying Dirichlet forms related to subordinate reflecting diffusions in non–smooth domains.

Abstract

Let Ω be a bounded domain with fractal boundary, for instance von Koch's snowflake domain. First we determine the range and the kernel of the trace on ∂Ω of Sobolev spaces of fractional order defined on Ω. This extends some earlier results of H. Wallin and J. Marschall Secondly we apply these results in studying Dirichlet forms related to subordinate reflecting diffusions in non–smooth domains.

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22 citations in Web of Science®
19 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Language:English
Date:2001
Deposited On:20 Feb 2012 15:03
Last Modified:05 Apr 2016 15:25
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0025-584X
Publisher DOI:https://doi.org/10.1002/1522-2616(200104)224:1<75::AID-MANA75>3.0.CO;2-N
Official URL:http://onlinelibrary.wiley.com/doi/10.1002/1522-2616%28200104%29224:1%3C75::AID-MANA75%3E3.0.CO;2-N/abstract
Other Identification Number:merlin-id:4433

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