Speaker
Reza Pakzad
Description
A theorem by Goldstein and Vodopyanov from 70s states the following: Let $\Omega \subset {\mathbb R}^n$ be a domain and $u : \Omega \to {\mathbb R}^n$ a deformation of $W^{1,n}$ regularity. If the Jacobian determinant ${\rm det}\, Du$ is positive almost everywhere, then $u$ is continuous. We will discuss a few recent generalizations of this theorem to other function spaces (such as fractional Sobolev spaces), and to the case when the codomain of $u$ is a smooth $n$-manifold with non-trivial topology rather than ${\mathbb R}^n$.