  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 $W^{2,2}$.
