A Schoenflies Extension Theorem for a Class of Locally Bi-lipschitz Homeomorphisms
نویسندگان
چکیده
In this paper we prove a new version of the Schoenflies extension theorem for collared domains Ω and Ω in Rn: for p ∈ [1, n), locally bi-Lipschitz homeomorphisms from Ω to Ω 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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