Remarks on Traces of $H^1$-functions Defined in a Domain with Corners | Graduate School of Mathematical Sciences, The University of Tokyo

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Remarks on Traces of $H^1$ -functions Defined in a Domain with Corners

J. Math. Sci. Univ. Tokyo
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
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

Abstract:
The set of traces of

$H^1(Î©)$ -functions on a part

$Î³$ of the boundary

$\rdÎ©$ is considered, where

$Î©$ is a bounded domain in

${\Bbb R}^2$ with a certain singularity, particularly, with corners at the end points of

$Î³$ . The aim of the present paper is to show that the set of all traces of functions in

$H^1(Î©)$ is equal algebraically and topologically to the domain of a certain fractional power of minus Laplacian on

$Î³$ 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

$Î©$ .

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

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Remarks on Traces of H1H^1-functions Defined in a Domain with Corners

Remarks on Traces of $H^1$ -functions Defined in a Domain with Corners