Sobolev Spaces on Non Smooth Domains and Dirichlet Forms Related to Subordinate Reflecting Diffusions
2001; Wiley; Volume: 224; Issue: 1 Linguagem: Inglês
10.1002/1522-2616(200104)224
ISSN1522-2616
Autores Tópico(s)Nonlinear Partial Differential Equations
ResumoMathematische NachrichtenVolume 224, Issue 1 p. 75-104 Original Paper Sobolev Spaces on Non Smooth Domains and Dirichlet Forms Related to Subordinate Reflecting Diffusions Walter Farkas, Walter Farkas [email protected] Universität München, Mathematisches Institut, Theresienstrasse 39, D–80333 München, GermanySearch for more papers by this authorNiels Jacob, Niels Jacob [email protected] University of Wales at Swansea, Department of Mathematics, Singleton Park, Swansea SA2 8PP, United KingdomSearch for more papers by this author Walter Farkas, Walter Farkas [email protected] Universität München, Mathematisches Institut, Theresienstrasse 39, D–80333 München, GermanySearch for more papers by this authorNiels Jacob, Niels Jacob [email protected] University of Wales at Swansea, Department of Mathematics, Singleton Park, Swansea SA2 8PP, United KingdomSearch for more papers by this author First published: 01 March 2001 https://doi.org/10.1002/1522-2616(200104)224:1 3.0.CO;2-NCitations: 20AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat 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. References [1] Adams, D.R., and Hedberg, L.I.: Function Spaces and Potential Theory, Springer–Verlag, Berlin, 1996 [2] Adams, D.R.: Traces of Potentials Arising from Translation Invariant Operators, Ann. Sc. Norm. Sup. 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