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 C 1 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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Gopalakrishnan, J., Qiu, W. Partial expansion of a Lipschitz domain and some applications. Front. Math. China 7, 249–272 (2012). https://doi.org/10.1007/s11464-012-0189-2
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DOI: https://doi.org/10.1007/s11464-012-0189-2
Keywords
- Lipschitz domain
- regular decomposition
- mixed boundary condition
- transversal vector field
- extension operator
- Schwarz preconditioner
- bounded cochain projector
- divergence
- curl
- Schöberl projector