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 ( ∂ Ω ) H^{s}(\partial \Omega ) . It is proved that the trace operator is a linear bounded operator from H s ( Ω ) H^{s}(\Omega ) to H s − 1 2 ( ∂ Ω ) H^{s-\frac {1}{2}}(\partial \Omega ) for 1 2 > s > 3 2 \frac {1}{2}>s>\frac {3}{2} .