Remarks on Traces of $H^1$-functions Defined in a Domain with Corners
Vol. 7 (2000), No. 2, Page 325--345.
Saito, Norikazu ; Fujita, Hiroshi
Remarks on Traces of $H^1$-functions Defined in a Domain with Corners
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Abstract:
The set of traces of $H^1(Ω)$-functions on a part $γ$ of the boundary $\rdΩ$ is considered, where $Ω$ is a bounded domain in ${\Bbb R}^2$ with a certain singularity, particularly, with corners at the end points of $γ$. The aim of the present paper is to show that the set of all traces of functions in $H^1(Ω)$ is equal algebraically and topologically to the domain of a certain fractional power of minus Laplacian on $γ$ with the zero boundary condition. The result is expected to be of use for the mathematical analysis of the DDM (domain decomposition method) applied to such $Ω$.
Keywords: trace theorem, non-smooth domain, fractional power of operator, domain decomposition method
Mathematics Subject Classification (1991): 46E35, 46C15
Mathematical Reviews Number: MR1768469
Received: 1999-05-10
