Zhuomin Liu, Mohammad Reza Pakzad
We prove the developability and C1,1/2 loc regularity of W2,2 isometric immersions of n-dimensional domains into Rn+1. As a conclusion we show that any such Sobolev isometry can be approximated by smooth isometries in the W2,2 strong norm, provided the domain is C1 and convex. Both results fail to be true if the Sobolev regularity is weaker than W2,2.
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