ABSTRACT
In this appendix we collect the function spaces that we consider in this book and prove some properties of the distance function x 7→ d(x, ∂Ω) when Ω is a sufficiently smooth (unbounded) domain.
Given an open set Ω ⊂ RN (even Ω = RN ), Cb(Ω) (resp. Cb(Ω), omitting the subscript “b” when Ω is bounded) denotes the space of all bounded and continuous functions f : Ω→ R (resp. f : Ω → R) and it is endowed with the sup-norm, i.e., ||f ||∞ = supx∈Ω |f(x)| for any f ∈ Cb(Ω) (resp. f ∈ Cb(Ω)).
