Remarks on Traces of H 1 -functions Defined in a Domain with Corners
Norikazu Saito, Hiroshi Fujita · Institutional Repositories DataBase (IRDB) · 2000
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 $Ω$.