A. Molchanova:

"Invertibility properties of Sobolev mappings";

Talk: PDE afternoon, TU Wien - University of Vienna, Wien; 2020-10-07.

We study weak limits of Sobolev homeomorphisms. It turns out to be that these mappings are invective almost everywhere in Sobolev exponent p>n−1. Otherwise, there exists even a strong limit of Sobolev homeomorphisms, such that the preimage of a point is a continuum for every point in a set of positive measure, and a topological image of a point is a continuum for every point in a set of positive measure in the domain. In the limiting case p=n−1 injectivity almost everywhere follows under certain additional assumption on the distortion of mappings.

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