Sponsor
This work was supported in part by the NSF under DMS-1014817
Published In
Frontiers of Mathematics in China
Document Type
Post-Print
Publication Date
2012
Subjects
Boundary value problems, Lipschitz domains, Regular decomposition, Vector fields, Decomposition (Mathematics)
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 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
Rights
Copyright © 2012, Higher Education Press and Springer-Verlag Berlin Heidelberg
Locate the Document
DOI
10.1007/s11464-012-0189-2
Persistent Identifier
http://archives.pdx.edu/ds/psu/10608
Citation Details
Published as: Gopalakrishnan, J., Qiu, W. Partial expansion of a Lipschitz domain and some applications. Front. Math. China 7, 249–272 (2012).
Description
This is an Author's Original Manuscript of an article whose final and definitive form, the Version of Record, has been published in the Frontiers of Mathematics in China, 2012, Vol. 7, Issue 2.