The closure of planar diffeomorphisms in Sobolev spaces

G. De Philippis; A. Pratelli

doi:10.1016/j.anihpc.2019.08.001

The closure of planar diffeomorphisms in Sobolev spaces

G. De Philippis, A. Pratelli

Mathematics

Research output: Contribution to journal › Article › peer-review

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 Müller and Spector.

Original language	English (US)
Pages (from-to)	181-224
Number of pages	44
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	37
Issue number	1
DOIs	https://doi.org/10.1016/j.anihpc.2019.08.001
State	Published - Jan 1 2020

Keywords

INV mappings
Non-crossing mappings
Sobolev approximation of mappings

ASJC Scopus subject areas

Analysis
Mathematical Physics
Applied Mathematics

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10.1016/j.anihpc.2019.08.001

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AU - Pratelli, A.

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AB - 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 Müller and Spector.

KW - INV mappings

KW - Non-crossing mappings

KW - Sobolev approximation of mappings

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The closure of planar diffeomorphisms in Sobolev spaces

Abstract

Keywords

ASJC Scopus subject areas

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