Partial expansion of a Lipschitz domain and some applications  

作　　者：Jay Gopalakrishnan Weifeng Qiu 

机构地区：[1]Department of Mathematics, Portland State University, Portland, OR 972,97, USA [2]Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, MN 55455, USA

出　　处：《Frontiers of Mathematics in China》2012年第2期249-272,共24页中国高等学校学术文摘·数学（英文）

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.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.

关 键 词：Lipschitz  domain regular decomposition mixed boundary condition transversal vector field extension operator Schwarz preconditioner bounded cochain projector divergence CURL SchSberl projector 

分 类 号：O177.3[理学—数学] TP317[理学—基础数学]