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

Authors:	Zhonghai Ding

Affiliation:	Department of Mathematics Texas A&M University College Station, Texas 77843

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 $H^{s}(partialOmega)$ . It is proved that the trace operator is a linear bounded operator from $H^{s}(Omega)$ to $H^{s-frac{1}{2}}(partialOmega)$ for $frac{1}{2}<s<frac{3}{2}$ .

Keywords:	Sobolev spaces Lipschitz domains trace theorem

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