Rigidity and regularity of co-dimension one Sobolev isometric immersions

Abstract

We prove the developability and $C^{1,1/2}$ regularity of $W^{2,2}$ isometric immersions of $n$-dimensional domains into $R^{n+1}$. As a conclusion we show that any such Sobolev isometry can be approximated by smooth isometries in the $W^{2,2}$ strong norm, provided the domain is $C^1$ and convex. Both results fail to be true if the Sobolev regularity is weaker than $W^{2,2}$.

43 pages, 15 figures

References in corpus (2)

• The von Karman equations for plates with residual strain
• Sobolev spaces of isometric immersions of arbitrary dimension and codimension

Cited by in corpus (2)

• Sobolev spaces of isometric immersions of arbitrary dimension and codimension
• Stability of isometric immersions of hypersurfaces