Uniform and Sobolev extension domains
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- by David A. Herron and Pekka Koskela PDF
- Proc. Amer. Math. Soc. 114 (1992), 483-489 Request permission
Abstract:
We prove that if a domain $D \subset {{\mathbf {R}}^n}$ is quasiconformally equivalent to a uniform domain, then $D$ is an extension domain for the Sobolev class $W_n^1$ if and only if $D$ is locally uniform. We provide examples which suggest that this result is best possible. We exhibit a list of equivalent conditions for domains quasiconformally equivalent to uniform domains, one of which characterizes the quasiconformal homeomorphisms between uniform and locally uniform domains.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 483-489
- MSC: Primary 46E35; Secondary 30C65
- DOI: https://doi.org/10.1090/S0002-9939-1992-1075947-1
- MathSciNet review: 1075947