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Sobolev Spaces on Non Smooth Domains and Dirichlet Forms Related to Subordinate Reflecting Diffusions
Author(s) -
Farkas Walter,
Jacob Niels
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200104)224:1<75::aid-mana75>3.0.co;2-n
Subject(s) - mathematics , sobolev space , pure mathematics , bounded function , fractal , dirichlet distribution , domain (mathematical analysis) , trace (psycholinguistics) , boundary (topology) , sobolev inequality , kernel (algebra) , sobolev spaces for planar domains , heat kernel , mathematical analysis , interpolation space , boundary value problem , functional analysis , biochemistry , chemistry , gene , linguistics , philosophy
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.