This work was supported in part by the NSF under DMS-1014817
Frontiers of Mathematics in China
Lipschitz domains, Regular decomposition
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
Qiu, Weifeng and Gopalakrishnan, Jay, "Partial Expansion of a Lipschitz Domain and Some Applications" (2012). Mathematics and Statistics Faculty Publications and Presentations. 40.