The closure of planar diffeomorphisms in Sobolev spaces

G. De Philippis, A. Pratelli

Research output: Contribution to journalArticle


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 languageEnglish (US)
Pages (from-to)181-224
Number of pages44
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Issue number1
StatePublished - Jan 1 2020



  • INV mappings
  • Non-crossing mappings
  • Sobolev approximation of mappings

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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