Partial expansion of a Lipschitz domain and some applications

作     者：Jay Gopalakrishnan Weifeng Qiu 

作者机构：Department of Mathematics Portland State University Portland OR 97297 USA Institute for Mathematics and Its Applications University of Minnesota Minneapolis MN 55455 USA 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2012年第7卷第2期

页      面：249-272页

核心收录：

学科分类：07[理学] 08[工学] 070104[理学-应用数学] 0835[工学-软件工程] 0701[理学-数学] 081202[工学-计算机软件与理论] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported in part by the NSF the support from the IMA (Minneapolis) 

主　　题：Lipschitz ,domain regular decomposition mixed boundary condition transversal vector field extension operator Schwarz preconditioner bounded cochain projector divergence curl SchSberl projector 

摘      要：We show that a Lipschitz domain can be expanded solely near a part of its boundary, assuming that the part is enclosed by a piecewise C1 curve. The expanded domain as well as the extended part are both Lipschitz. We apply this result to prove a regular decomposition of standard wector Sobolev spaces with vanishing traces only on part of the boundary. Another application in the construction of low-regularity projectors into finite element spaces with partial boundary conditions is also indicated.