Anastasia Molchanova - Limits of Sobolev homeomorphisms: global injectivity

The weak (or even uniform) limits of homeomorphisms are known to fail to be homeomorphic. Nevertheless, one could ask for a weaker notion of invertibility, such as injectivity almost everywhere 'in image', i.e. almost all points in the image have only one preimage, or 'in domain', i.e. the restriction of the mapping on the domain without some null-set is injective. In this talk, we consider the question when limits of Sobolev homeomorphisms are injective almost everywhere in both cases - in image and in domain.