Title: Prescribing the approximate derivative of homeomorphisms
Abstract: Study of the interplay between topological and analytical properties of homeomorphisms equipped with a derivative goes back to works of John Ball in nonlinear elasticity. We will see that, under mild assumptions, it is possible to find an almost everywhere (a.e.) approximately differentiable homeomorphism of the Euclidean unit cube with a given (prescribed) derivative a.e. Moreover, this homeomorphism equals identity on the boundary of the unit cube and preserves sets of measure zero.
I will discuss the connections of this result with some recent results about Sobolev homeomorphisms and show a few highlights of the proof. This is joint work with Paweł Goldstein (University of Warsaw) and Piotr Hajłasz (University of Pittsburgh).
