Frontiers of Mathematics in China >
Partial expansion of a Lipschitz domain and some applications
Received date: 24 Jan 2011
Accepted date: 04 Jul 2011
Published date: 01 Apr 2012
Copyright
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 vector 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.
Jay Gopalakrishnan , Weifeng Qiu . Partial expansion of a Lipschitz domain and some applications[J]. Frontiers of Mathematics in China, 2012 , 7(2) : 249 -272 . DOI: 10.1007/s11464-012-0189-2
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