AN EXAMPLE ON SOBOLEV SPACE APPROXIMATION

Abstract

For each d[ges ]2 we construct a connected open set Ω⊂ℝ^d such that Ω=int (clos(Ω)), and for each k[ges ]1 and each p∈[1, +∞), the subset W^{k, ∞}(Ω) fails to be dense in the Sobolev space W^{k, p}(Ω), in the norm of W^{k, p}(Ω).