Title: The Internal Douglas Condition
Abstract: The Sobolev Jordan-Schönflies problem asks a simple question: When does an embedding of the unit circle into the plane admit a homeomorphic extension in the Sobolev space W^1,p? Such a question is of basic interest in Nonlinear Elasticity, where Sobolev homeomorphisms describe an acceptable class of deformations between two elastic bodies. In a recent but important development, we have discovered an if and only if condition called the Internal Douglas Condition which gives a pleasingly complete answer to this problem in the planar case. In this talk, we will discuss this result and the related works leading up to it. This talk is based on joint work with Jani Onninen and Haiqing Xu.
