2020-08-04T20:39:02Zhttps://repository.dl.itc.u-tokyo.ac.jp/?action=repository_oaipmhoai:repository.dl.itc.u-tokyo.ac.jp:000402352020-07-10T06:57:17Z00312:06865:07017:0702300009:00504:06868:07019:07024
Remarks on Traces of $H^1$-functions Defined in a Domain with Cornersengtrace theoremnon-smooth domainhttp://hdl.handle.net/2261/1210Departmental Bulletin PaperSaito, NorikazuThe 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 $Ω$.Journal of mathematical sciences, the University of Tokyo72325345200013405705AA11021653application/pdf415https://repository.dl.itc.u-tokyo.ac.jp/?action=repository_action_common_download&item_id=40235&item_no=1&attribute_id=19&file_no=1Graduate School of Mathematical Sciences, The University of Tokyo2017-06-14