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 $H^{s}(\partial\Omega)$. 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 $\frac{1}{2}<s<\frac{3}{2}$.