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Proceedings of the American Mathematical Society

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ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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A proof of the trace theorem of Sobolev spaces on Lipschitz domains
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by Zhonghai Ding PDF
Proc. Amer. Math. Soc. 124 (1996), 591-600 Request permission

Abstract:

A complete proof of the trace theorem of Sobolev spaces on Lipschitz domains has not appeared in the literature yet. The purpose of this paper is to give a complete proof of the trace theorem of Sobolev spaces on Lipschitz domains by taking advantage of the intrinsic norm on $H^{s}(\partial \Omega )$. It is proved that the trace operator is a linear bounded operator from $H^{s}(\Omega )$ to $H^{s-\frac {1}{2}}(\partial \Omega )$ for $\frac {1}{2}<s<\frac {3}{2}$.
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Additional Information
  • Zhonghai Ding
  • Affiliation: Department of Mathematics Texas A&M University College Station, Texas 77843
  • Address at time of publication: Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, Nevada 89154
  • Email: dingz@nevada.edu
  • Received by editor(s): September 15, 1994
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 591-600
  • MSC (1991): Primary 46E35
  • DOI: https://doi.org/10.1090/S0002-9939-96-03132-2
  • MathSciNet review: 1301021