Calculus of Variations and Geometric Measure Theory

The Sobolev closure of planar diffeomorphisms

Aldo Pratelli (University of Pisa)

created by gelli on 30 Sep 2019

2 oct 2019 -- 17:00   [open in google calendar]

Sala Seminari Dipartimento di Matematica di Pisa


We will discuss about the well-studied problem of finding the class of planar mappings which can be approximated by diffeomorphisms in the Sobolev norm. It has been proved in the last years that approximation is possible for all Sobolev homeomorphisms, but it is simple to notice that some non-injective or non-surjective maps can be approximated as well, and this motivated the definition of INV mappings, done in the '90s by Müller and Spector. A reasonable conjecture was that INV mappings were exactly the closure of diffeomorphisms, but it has been recently shown that the correct class is actually smaller, namely, the class of non-crossing mappings. Some properties of this class have been also proved recently. Based on joint works with G. De Philippis, D. Campbell, E. Radici.