Approximation of Piecewise Affine Homeomorphisms by Diffeomorphisms

We prove that any countably piecewise affine homeomorphism from an open set of ℝ 2 can be approximated, together with its inverse, by diffeomorphisms in the W 1, p and the L ∞ norms.

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Bibliographic Details
Published in:	The Journal of geometric analysis Vol. 24; no. 3; pp. 1398 - 1424
Main Authors:	Mora-Corral, Carlos, Pratelli, Aldo
Format:	Journal Article
Language:	English
Published:	Boston Springer US 01-07-2014
Subjects:	Abstract Harmonic Analysis Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics 57Q55 Approximation of homeomorphisms Piecewise affine homeomorphisms 41A30 Diffeomorphisms 41A29
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Description
Summary:	We prove that any countably piecewise affine homeomorphism from an open set of ℝ 2 can be approximated, together with its inverse, by diffeomorphisms in the W 1, p and the L ∞ norms.
ISSN:	1050-6926 1559-002X
DOI:	10.1007/s12220-012-9378-1