## 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
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 $Î©$.