2021-09-22T21:26:58Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000402352021-03-01T21:04:35ZRemarks on Traces of $H^1$-functions Defined in a Domain with CornersSaito, Norikazu138833415trace theoremnon-smooth domainapplication/pdfThe 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 $Ω$.departmental bulletin paperGraduate School of Mathematical Sciences, The University of Tokyo2000application/pdfJournal of mathematical sciences, the University of Tokyo27325345AA1102165313405705https://repository.dl.itc.u-tokyo.ac.jp/record/40235/files/jms070207.pdfeng