Partial expansion of a Lipschitz domain and some applications

@article{Gopalakrishnan2011PartialEO,
  title={Partial expansion of a Lipschitz domain and some applications},
  author={Jay Gopalakrishnan and Weifeng Qiu},
  journal={Frontiers of Mathematics in China},
  year={2011},
  volume={7},
  pages={249-272}
}
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… 

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