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Partial Expansion of a Lipschitz Domain and Some Applications
Frontiers of Mathematics in China
  • Weifeng Qiu, University of Minnesota - Twin Cities
  • Jay Gopalakrishnan, Portland State University
Document Type
Publication Date
  • 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


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. Copyright Springer and available online at:

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Weifeng Qiu and Jay Gopalakrishnan. "Partial Expansion of a Lipschitz Domain and Some Applications" Frontiers of Mathematics in China (2012)
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