A Schoenflies extension theorem for a class of locally bi-Lipschitz homeomorphisms

Details A Schoenflies extension theorem for a class of locally bi-Lipschitz homeomorphisms A Schoenflies extension theorem for a class of locally bi-Lipschitz homeomorphisms

2010-08-20

arxiv.org/abs/1008.3544v1

Mathematics

Analysis of PDEs

15 pages, 3 figures

Scientific paper

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.

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