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Diffeomorphic approximation of W-1,W-1 planar Sobolev homeomorphisms

Publication at Faculty of Mathematics and Physics |
2018

Abstract

Let Omega subset of R-2 be a domain and let f is an element of W-1,W-1 (Omega, R-2) be a homeomorphism (between Omega and f(Omega)). Then there exists a sequence of smooth diffeomorphisms f(k) converging to f in W-1,W-1 (Omega, R-2) and uniformly.