Equivalent Characterizations and Applications of Fractional Sobolev Spaces with Partially Vanishing Traces on $(\epsilon ,\delta ,D)$-Domains Supporting $D$-Adapted Fractional Hardy Inequalities

Jun Cao, Dachun Yang, Qishun Zhang

Let $\Omega \subset {\mathbb{R}}^n$ be an $(\epsilon ,\delta ,D)$-domain, with $\epsilon \in (0,1]$, $\delta \in (0,\infty ]$, and $D\subset \partial \Omega$ being a closed part of $\partial \Omega$, which is a general open connec…