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Partial expansion of a Lipschitz domain and some applications

Frontiers of Mathematics in China volume 7, pages 249–272 (2012)Cite this article

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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Authors and Affiliations

  1. Department of Mathematics, Portland State University, Portland, OR, 97207, USA

    Jay Gopalakrishnan

  2. Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, MN, 55455, USA

    Weifeng Qiu

Authors
  1. Jay Gopalakrishnan
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  2. Weifeng Qiu
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Correspondence to Weifeng Qiu.

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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

MSC

  • 65L60
  • 65N30
  • 46E35
  • 52B10
  • 26A16