Diffeomorphic approximation of planar Sobolev homeomorphisms in Orlicz–Sobolev spaces.

Let Ω ⊆ R 2 be a domain, let Φ be a Δ 2 Young function and let f ∈ W 1 , Φ ( Ω , R 2 ) be a homeomorphism between Ω and f ( Ω ) . Then there exists a sequence of diffeomorphisms f k converging to f in the Sobolev–Orlicz space W 1 , Φ ( Ω , R 2 ) . Further for an injective continuous map φ ∈ W 1 , Φ ( ∂ ( − 1 , 1 ) 2 , R 2 ) we find a diffeomorphism in W 1 , Φ ( ( − 1 , 1 ) 2 , R 2 ) that equals φ on the boundary. [ABSTRACT FROM AUTHOR]