I think I found a proof, that on Lipschitz domains $\Omega$, $H^{1+s}(\Omega)$ is the dual space of $H^{1-s}(\Omega)$ with respect to the $H^1(\Omega)$ scalar product for all $0\leq s<1/2$. Does anyone know a reference to such a result? (I am assuming that $H^r(\Omega)$ is defined by interpolation between $L^2(\Omega)$, $H^1(\Omega)$, and $H^2(\Omega)$).