A proof of the trace theorem of Sobolev spaces on Lipschitz domains

Author:
Zhonghai Ding

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

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Abstract | References | Similar Articles | Additional Information

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

Keywords:
Sobolev spaces,
Lipschitz domains,
trace theorem

Received by editor(s):
September 15, 1994

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1996
American Mathematical Society