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

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 $\frac {1}{2}<s<\frac {3}{2}$.