Necessary and sufficient conditions of compactness of certain embeddings of Sobolev spaces

Necessary and sufficient conditions on an open set Ω ⊂ ℝn are obtained ensuring that for l,m ∈ 0, m < l the embedding W∞l ⊂ W∞m(Ω) is compact, where W∞m(Ω) is the Sobolev space and W∞l(Ω) is the closure in W∞l(Ω) of the space of all infinitely continuously differentiable functions on Ω with supports compact in Ω. © 2019 The L.N. Gumilyov Eurasian National University.