This work was supported in part by the NSF under DMS-1014817
Frontiers of Mathematics in China
Boundary value problems, Lipschitz domains, Regular decomposition, Vector fields, Decomposition (Mathematics)
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
Copyright © 2012, Higher Education Press and Springer-Verlag Berlin Heidelberg
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Published as: Gopalakrishnan, J., Qiu, W. Partial expansion of a Lipschitz domain and some applications. Front. Math. China 7, 249–272 (2012).