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 by pratelli on 17 Dec 2019


Accepted Paper

Inserted: 19 oct 2017
Last Updated: 17 dec 2019

Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Year: 2019

ArXiv: 1710.07228 PDF


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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