A necessary condition for Sobolev extension domains in higher dimensions

Miguel García-Bravo, Tapio Rajala, Jyrki Takanen

We give a necessary condition for a domain to have a bounded extension operator from $L^{1,p}(\Omega )$ to $L^{1,p}({\mathbb{R}}^n)$ for the range $1<p<2$. The condition is given in ter…