English

Partial expansion of a Lipschitz domain and some applications

Analysis of PDEs 2012-01-04 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1201.0047,
  title  = {Partial expansion of a Lipschitz domain and some applications},
  author = {Jay Gopalakrishnan and Weifeng Qiu},
  journal= {arXiv preprint arXiv:1201.0047},
  year   = {2012}
}