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Partial expansion of a Lipschitz domain and some applications |
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| Authors: | Jay Gopalakrishnan Weifeng Qiu |
| Affiliation: | 1. Department of Mathematics, Portland State University, Portland, OR 97207, USA; 2. Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, MN 55455, USA |
| 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. |
| Keywords: | Lipschitz domain regular decomposition mixed boundary condition transversal vector field extension operator Schwarz preconditioner bounded cochain projector divergence curl Sch?berl projector |
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