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arXiv · 2401.06253

Regularity of Finite Energy Deformations

Daniel Rosenblatt
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Abstract

We review results of {\v{S}}ver\'{a}k, and Goldstein-Haj{\l}asz-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 {\v{S}}ver\'{a}k's proof to a co-dimension 1 case.

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Daniel Rosenblatt. 2024-01-11. Regularity of Finite Energy Deformations. https://arxiv.org/abs/2401.06253

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