Calculus of Variations and Geometric Measure Theory
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G. De Philippis - A. Pratelli

The closure of planar diffeomorphisms in Sobolev spaces

created by dephilipp on 19 Oct 2017
modified on 30 Oct 2017

[BibTeX]

Preprint

Inserted: 19 oct 2017
Last Updated: 30 oct 2017

Year: 2017

ArXiv: 1710.07228 PDF

Abstract:

We characterize the (sequentially) weak and strong closure of planar diffeomorphisms in the Sobolev topology and we show that they always coincide. We also provide some sufficient condition for a planar map to be approximable by diffeomorphisms in terms of the connectedness of its counter-images, in the spirit of Young's characterisation of monotone functions. We finally show that the closure of diffeomorphisms in the Sobolev topology is strictly contained in the class INV introduced by Muller and Spector.


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