A Trace Result for Sobolev Functions on Planar Jordan Domains

Overview & Synopsis

After recalling some facts from Hausdorff measure theory, we define, using the notion of $s-$length, the space $L^p(\partial\Omega, \mathop{\rm d}\sigma^s)$ on the boundary of a Jordan domain $\Omega$. Then, with the aid of some auxiliary considerations, we establish a trace result for Sobolev's space functions $W^{1,p}(\Omega)$, $1 < p 1$. This result generalizes the classical case for Lipschitz regular domains.