Abstract
In this talk, we discuss the weak limits of Sobolev homeomorphisms and their injectivity properties. We show that these mappings are almost everywhere injective when the Sobolev exponent p>n−1. In the critical case p=n−1, injectivity almost everywhere can still be guaranteed under specific coercivity conditions. For p≤n−1, we provide an example where the strong limit of homeomorphisms fails to preserve injectivity.
Brief Biography
Dr. Anastasia Molchanova obtained her Ph.D.in December 2016 at the Sobolev Institute of Mathematics in Russia. Since then, she has conducted research at the Sobolev Institute, Novosibirsk State University (Russia), the University of Vienna, and TU Wien (Austria). Currently, she holds a senior postdoctoral position at the Institute of Analysis and Scientific Computing at TU Wien, where she leads her own FWF Elise Richter project.
