ABSTRACT
In this appendix we collect some regularity results of the distance function d(x) = dist(x, ∂Ω), when ∂Ω is the boundary of a smooth open subset Ω of RN . We limit ourselves to state them in the case when Ω is bounded since they are classical results (see, e.g., [66, Section 14.6]). Moreover, we show that most of them may be extended also to the case where Ω is unbounded. The results we present here are taken from [59].
