Diffeomorphic approximation of planar Sobolev homeomorphisms in Orlicz Sobolev spaces

摘要

Let Omega subset of R-2 be a domain, let Phi be a Delta(2) Young function and let f is an element of W-1,W-Phi(Omega, R-2) be a homeomorphism between Omega and f(Omega). Then there exists a sequence of diffeomorphisms f(k) converging to f in the Sobolev-Orlicz space W-1,W-Phi(Omega, R-2). Further for an injective continuous map phi is an element of W-1,W-Phi (partial derivative(-1,1)(2), R-2) we find a diffeomorphism in W-1,W-Phi((-1,1)(2), R-2) that equals phi on the boundary. (C) 2017 Elsevier Inc. All rights reserved.