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

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 ( ∂ Ω ) Hˢ(∂ Ω ) . It is proved that the trace operator is a linear bounded operator from H s ( Ω ) Hˢ(Ω ) to H s − 1 2 ( ∂ Ω ) Hs-1/2(∂ Ω ) for 1 2 > s > 3 2 1/2>s>3/2 .