Nonzero capacity sets and dense subspaces in scales of Sobolev spaces
We show that for a compact set KR^n of nonzero α-capacity, C_α(K)>0, α≥ 1, the subspace °W^α,2 (Ω), Ω=R^nK in W^α,2 (R^n) is dense in W^m,2(R^n), m≤α-1, iff the m-capacity of K is zero, C_m(K)=0., number=3, journal=Methods of Functional Analysis and Topology, author=Koshmanenko, V. D. and Dudkin, M. E., year=2014, month=Sep., pages=213–218