On the closure of planar diffeomorphisms and non-crossing functions

Aldo Pratelli (Erlangen)

ABSTRACT: We will discuss the question if and how  a Sobolev planar map can be approximated, in Sobolev norm, 
with a sequence of diffeomorphisms. This is important for some applications, in particular in the context of 
nonlinear elasticity. We will describe the history of the problem, the partial answers given in the years, 
and a characterization found only very recently. The question is quite analytical, but many arguments in the 
proofs are of geometric flavour. The talk will not be too technical, and accessible for mathematicians of any area. 

Joint work with G. De Philippis.