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