Publication: Sobolev spaces on non-smooth domains and Dirichlet forms related to subordinate reflecting diffusions
Sobolev spaces on non-smooth domains and Dirichlet forms related to subordinate reflecting diffusions
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Farkas, W., & Jacob, N. (2001). Sobolev spaces on non-smooth domains and Dirichlet forms related to subordinate reflecting diffusions. Mathematische Nachrichten, 224(1), 75–104. https://doi.org/10.1002/1522-2616(200104)224:1<75::AID-MANA75>3.0.CO;2-N
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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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- Jacob, Niels
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Farkas, W., & Jacob, N. (2001). Sobolev spaces on non-smooth domains and Dirichlet forms related to subordinate reflecting diffusions. Mathematische Nachrichten, 224(1), 75–104. https://doi.org/10.1002/1522-2616(200104)224:1<75::AID-MANA75>3.0.CO;2-N