Superposition operator in Sobolev spaces on domain

Abstract

For an arbitrary open set Ω ⊂ ℝn we characterize all functions G on the real line such that G o u ∈ W1,p(Ω) for all u ∈ W1,p. New element in the proof is based on Maz'ya's capacitary criterion for the imbedding W1,p(Ω) → L∞(Ω). Show more