Regularity of Finite Energy Deformations
Abstract
We review results of Sver\'ak, and Goldstein-Hajasz-Pakzad on how to show the continuity of functions in a critical Sobolev space with positive Jacobian. In the final chapter we expand on the theory of VMO functions, showing a version of the change of variables theorem in this regularity, which generalizes the first step in Sver\'ak's proof to a co-dimension 1 case.
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