  In this paper we prove a new version of the Schoenflies extension theorem for
collared domains in Euclidean n-space: for 1 < p < n, locally bi-Lipschitz
homeomorphisms between collared domains with locally p-integrable, second-order
weak derivatives admit homeomorphic extensions of the same regularity.
Moreover, the theorem is essentially sharp. The existence of exotic 7-spheres
shows that such extension theorems cannot hold for p > n = 7.
