On p. 5957 l. 31: Say "a bounded open connected set (i.e. bounded domain)" instead of "an open bounded set". This assumption is required for the Poincare's inequality to hold. It is clear that this assuption of connectness can be relaxed; The point is not to allow $\Omega$ have a component $\Omega'$, such that $\partial \Omega' \subset \Gamma_1$.
The conference slides are here.