Partial expansion of a Lipschitz domain and some applications

Details Partial expansion of a Lipschitz domain and some applications Partial expansion of a Lipschitz domain and some applications

2011-12-30

arxiv.org/abs/1201.0047v1

Frontiers of Mathematics in China, 2012

Mathematics

Analysis of PDEs

Scientific paper

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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