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Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms. (English) Zbl 1348.37071

Summary: We show that a planar bi-Lipschitz orientation-preserving homeomorphism can be approximated in the \(W^{1, p}\) norm, together with its inverse, with an orientation-preserving homeomorphism which is piecewise affine or smooth.

MSC:

37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
74B20 Nonlinear elasticity
26A16 Lipschitz (Hölder) classes
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